Tenebrae on Palm Sunday? Do you mean Matins/Lauds for Palm Sunday? I believe Tenebrae is a special form of Matins/Lauds used only on Maundy Thursday through Holy Saturday.

oh. hmmmm. Could one conceivably turn Matins/Lauds for Palm Sunday into a Tenebrae service? From what I gather, the Tenebrae service is varied and flexible. I get more confused the more I research it.

There is Tenebrae which is Matins/Lauds for the Triduum.

But, there are also "Tenebrae" services which one frequently encounters in Cathedrals in the USA which are nothing more than Lessons and Carols for Holy Week. This is NOT Tenebrae.

You could consider doing something like the "Four Last Words".

This past Palm Sunday St. Peter's Cathedral in Kansas City, KS, had a "Tenebrae" service of the kind to which Salieri referred. Perhaps Kevin Vogt of St. Michael's in Leawood, KS, could provide the OP a program.

The folks with whom the word "Tenebrae" are likely to resonate will likely be the same folk who would view labelling a service done on the evening of Palm Sunday as "Tenebrae" as an argument rather than as an invitation. Nor would they likely welcome importing the hearse and candles into such a service.

Tenebrae as such no longer exists in the post-conciliar liturgy of the hours. So even if you do Tenebrae during the Triduum (unless your community follows the pre-reform LOH) you still don't really have Tenebrae in a purist sense. It simply doesn't exist any more. So I see the argument about whether to have it on Palm Sunday or during the Triduum as something of a moot point.
I suppose you can still argue whether we should have things called Tenebrae at all, now that it is no longer in the official books. For me, the antiphons and lessons and psalmody (and the musical settings of those parts) is so rich that it seems like a terrible loss to simply discard it. Would I prefer to throw it all away aside from concert use, or place it in the context of a devotional service (albeit a somewhat manufactured one)? I'd rather keep something of what is old - I like the phrase "creative conservation."
Also, to the best of my knowledge the word Tenebrae itself is a popular title rather than an official title given by the Church to Lauds/Matins during the Triduum. I see no reason the idea or ethos of Tenebrae cannot live on as a devotional service.

Liam - established Tenebrae services at Ordinary Form cathedrals are actually quite popular. For example, the Seattle, Columbus, and St Louis Cathedrals among others hold some such service.

Here's what Paschale solemnitatis says about it:

40. It is recommended that there be a communal celebration of the Office of Readings and Morning Prayer on Good Friday and Holy Saturday. It is fitting that the bishop should celebrate the Office in the cathedral, with as far as possible the participation of the clergy and people.[45]

This Office, formerly called "Tenebrae," held a special place in the devotion of the faithful as they meditated upon the passion, death and burial of the Lord, while awaiting the announcement of the resurrection.

Should be fine to do it your way, though I personally would only do it on Maundy Thursday, Good Friday, and Holy Saturday.

I've only witnessed Tenebrae on the evening of Spy Wednesday (my favorite experience of it was in English at the Episcopal monastery of the Society of St John the Evangelist on the Charles River in Cambridge MA - the monks do it up right, and the service is well attended) or during the Triduum. I would say that Good Friday evening is likely the most opportune time for it, especially if your parish celebrates the divine liturgy at 3PM.