Well, the Blessed Sacrament would not be *exposed* (i.e., in a monstrance), but it would be in the place of reservation and public adoration would be suitable until the church is closed that evening.

Silence is golden, but he who has the gold makes the rules.

We don't silence the organ, but use it only to accompany singing for Holy Thursday and Good Friday. There are no instrumental pieces played - interesting to me since the local Trad mass plays preludes and postludes all through Lent. Their reasoning is that both are not part of the mass. I think that violates the spirit, if not the letter, of the regulations. Go figure. However, there is silence after Repose Holy Thursday with adoration until 10:00 p.m. - midnight or so when the building is locked.

The consensus around here, based on custom I think, is that silence should be kept.

I would like to concur, in part, and dissent in part.

Just as the consecration is spoken in an extremely quiet voice, and just as music is not permitted* at that point, it is reasonable that the custom of silence should be maintained during this most unusual of evenings.

A local parish hereabouts has a sign posted at the entrance to the adoration chapel. It notes that that there will be [in the directive sense, not the descriptive] a rosary, a divine mercy chaplet and then.... silent prayer for the balance of the hour.

I had not (until recently) thought about the singing of part of the Divine Office, but this would make eminent sense. I can think of other music which would be appropriate (but unlike others here, I do most emphatically think that Taize is appropriate.

Let's see what the relavant part of the Roman Missal has to say and then some personal opinions:

The Transfer of the Most Blessed Sacrament
37. A fter the Prayer after Communion, the Priest puts incense in the thurible while standing, blesses it and then, kneeling, incenses the Blessed Sacrament three times. Then, having put on a white humeral veil, he rises, takes the ciborium, and covers it with the ends of the veil.
38. A procession is formed in which the Blessed Sacrament, accompanied by torches and incense, is carried through the church to a place of repose prepared in a part of the church or in a chapel suitably decorated. A lay minister with a cross, standing between two other ministers with lighted candles leads off. Others carrying lighted candles follow. Before the Priest carrying the Blessed Sacrament comes the thurifer with a smoking thurible. Meanwhile, the hymn Pange, lingua (exclusive of the last two stanzas) or another eucharistic chant is sung.
39. When the procession reaches the place of repose, the Priest, with the help of the Deacon if necessary, places the ciborium in the tabernacle, the door of which remains open. Then he puts incense in the thurible and, kneeling, incenses the Blessed Sacrament, while Tantum ergo Sacramentum or another eucharistic chant is sung. Then the Deacon or the Priest himself places the Sacrament in the tabernacle and closes the door.
40. A fter a period of adoration in silence, the Priest and ministers genuflect and return to the sacristy.
41. A t an appropriate time, the altar is stripped and, if possible, the crosses are removed from the church. It is expedient that any crosses which remain in the church be veiled.
42. V espers (Evening Prayer) is not celebrated by those who have attended the Mass of the Lord’s Supper.
43. T he faithful are invited to continue adoration before the Blessed Sacrament for a suitable length of time during the night, according to local circumstances, but after midnight the adoration should take place without solemnity.
44. I f the celebration of the Passion of the Lord on the following Friday does not take place in the same church, the Mass is concluded in the usual way and the Blessed Sacrament is placed in the tabernacle.

Now the important bit is #42 and especially 43.

43 seems to suggest that adoration should be held WITH solemnity prior to midnight.
Now to get an idea what that may mean you won't find the answer in the GIRM or the Missal, you need to instead take a look at "Order for the Solemn Exposition of the Holy Eucharist" (usually a green book) and "Holy Communion and Worship Of the Eucharist Outside Mass" (often an ugly tan cover). Both of those go into more detail regarding what is fitting for an organized, solemn form of adoration.

Compline (Night Prayer, in the Liturgy of the Hours) seems to be an option. The singing of chant, Eucharistic hymns, and other suitable songs also would seem to be an option.

(Other than the Liturgy of the Hours/Divine Office the only place hymn singing traditionally is part of Catholic prayer is during paraliturgical devotions like Eucharistic adoration.)

If I were organizing such a thing I would want a substantial period of silence, perhaps followed by some form of singing, perhaps some silence, then perhaps Compline. I would likely keep the music simple enough that it can be comfortably sung acappela, though since this is not part of the liturgy that isn't an absolute requirement.

In Rome (yes, that Rome, the one with the Pope) the custom is that people will visit several different churches and chapels on the evening of Holy Thursday and perhaps on Good Friday. The "Seven Churches" or Visita Iglesia as it is sometimes called. Indulgences were attached. Praying the traditional indulgence prayers for the Pope would have been part of the practice, as would in some instances the Stations of the Cross. Some people went individually, others went as a group in something like a procession. These are not exactly carried out in strict silence, as you might imagine. Don't think it is either necessary or traditional to kneel before the Blessed Sacrament in perfect silence and stillness for three hours without blinking or you go to hell or anything like that.

At Walsingham adoration at the Altar of Repose lasts until sometime in Good Friday morning. This is ancient custom which, apparently, some (quite a few?) nowadays would consider a novelty. But, surely Walsingham is not alone in this - there must be others.

As a 4th Degree Knight, we stand guard at the place of repose until midnight. Then our pastor removes the Lord and locks the church.

Point taken, Liam, but Our Lord is publicly reposed for adoration, then.

he who has the gold makes the rules decides which rules he will observe and ignore.

Fixed.

I wish Sacrosanctum Concilium # 23 had been created as # 0
because nobody ever reads beyond # 14 (and # 30 explains # 14).

Chris Garton-Zavesky
Compline/Night Prayer is still good to go, but Vespers/Evening Prayer is out for those attending the mass that evening.
Singing a bit of chant seems reasonable to me and within the rubrics so far as I can determine.

This might be of interest.

Yes, it's used by the Holy Land Franciscans. Having never experienced it, I couldn't answer your question about the readings. I would like to be in the Holy Land for Triduum one year.

Not your problem, but for the period you are away at Mass, it would presumably be appropriate for whoever 'takes over' to lead Evening Prayer. Evening Prayer has the opportunity for long reflective silences between most of the elements.

well to be historically accurate it might be fitting that we all fall asleep because we can't even stay awake and pray for one hour with our Lord

Matthew 26:40

Remember too that Jesus and his apostles sang a hymn before heading to the Mount of Olives. Matthew 26:30

One of us would have to escape, and be wearing nothing but a loin cloth

Already been done. It was called, "streaking."

and some visitor to the church would have to lose his ear.

I could easily provide a choir member who has lost his ear.

Remember too that Jesus and his apostles sang a hymn

Maybe they sang, "In the Garden." ;-) I suspect they sang a psalm.

So many things in scripture that I wish presented much more detailed information.

Do we know what the hymn is likely to have been?

I believe it would have been the great Hallel which was prayed on Passover. But I will need to check that.

An excellent article, which has been cited here before:

http://www.thesacredpage.com/2009/04/what-did-jesus-sing-at-last-supper.html