At our parish, when one of the ladies occasionally plays organ during low Mass, it is done as follows:

1. During the procession in. The organ music ends before the prayers at the foot of the Altar begin (perhaps ending while the priest is placing the chalice on the Altar and opening the Missale). There is no limit to how early before Mass you can start playing.

2. After the Offertory Proper is said, until the Orate Fratres.

3. During the distribution of Communion, until the Communion Antiphon is read.

4. After the prayers after Low Mass have been finished.

The general governing rule we follow is that the organ is not played while the Priest prays audibly, and not played during the Canon of the Mass at all, since that is a sacred silence.

It's been nearly twenty years, but...
One can play continuously up to the Gospel. Look for the missal being transported.
Then, one can play continuously up to the Sursum Corda.
After the celebrant begins the Sanctus, one can play up to the warning bell, but silence is preferred. After the second elevation, one can play, but silence is preferable. If playing, cease for the Ecce Agnus. Then resume.
I played a few masses with semi-continuous hymn singing (English) because the celebrant was saying the Latin Mass. The hymn singing stopped and started like the organ music outlined above.
But, various dioceses had different regulations, and what was done in the wild, wild west was considered degenerate by some.

The pertinent regulations can be found in De musica sacra et sacra liturgia:

It must be noted that if any local custom of playing the organ during Low Mass might interfere with the participation of the faithful, either by common prayer or song, the custom is to be abolished. This applies not only to the organ, but also to the harmonium or any other musical instrument which is played without interruption. Therefore, in such Masses, there should be no instrumental music at the following times:
a. After the priest reaches the altar until the Offertory;
b. From the first versicles before the Preface until the Sanctus inclusive;
c. From the Consecration until the Pater Noster, where the custom obtains;
d. From the Pater Noster to the Agnus Dei inclusive; at the Confiteor before the Communion of the faithful ; while the Postcommunion prayer is being said, and during the Blessing at the end of the Mass. (29)

So, when solo organ playing is permitted, it can be played at the entrance until the beginning of the Mass, at the Offertory, after the Sanctus until the Consecration, between the Agnus Dei and prayers before the people's Communion, and during Communion up until the priest reads the antiphon and Postcommunion. There can also be music before and after Mass. Yes, singing (Latin or vernacular) is also fine at any of those times. Formerly, elevation voluntaries were actually played during the Consecration, but that practice is no longer permitted according to the same document (27e). Music after the Elevation is tolerated but not recommended (14c, 27f, 29c).

The continuous playing someone mentioned above, and which is also referred to in paragraph 29, was formerly common in many places, as were Low Masses where the priest's prayers were completely inaudible to the congregation. You may still encounter them here and there, but it's no longer "best practice."