On what day of the week did Thomas first meet the resurrected Christ?

The answer to the OP question is - Tuesday.

After his crucifixion and death, Jesus was buried late on Friday evening in the sepulchre John 19:42. Early on Sunday morning (the third day) John 20:1 the women, then Peter and John, found the sepulchre empty after which Jesus appeared, first, to Mary Magdalene John 20:16

Late on that same day, the first day of the week (Sunday) Jesus appeared to the ten, Thomas being absent John 20:19. After a further eight days, he appeared again to all eleven John 20:26.

Some have attempted to say that Thomas was the eighth apostle and that this is relevant but the facts do not support this theory. The table on Wikipedia plainly shows that in all five accounts (Matthew, Mark, Luke, John and Acts) Thomas is numbered seventh.

After the appearance to the ten on the third day, there is a pause of eight full days ("after eight days"). The next day, therefore, is the twelfth day, numbered from the death of Jesus Christ.

So Jesus appeared to Thomas on the twelfth day, which would have been a Tuesday.

Since Thomas had been absent, he was not (yet) a witness of the resurrection of Jesus. But he was an apostle. So on the twelfth day - a significant day - Jesus appears again and Thomas, calling him 'My Lord and My God' testifies to the fact of the resurrection of Jesus Christ.

Whatever the reason for his absence, and whatever the reason for his doubting, Thomas, neveretheless, together with his fellow apostles, receives a visitation on the twelfth day of Jesus' rising from the dead - a significant event. And there were twelve present, Jesus and the eleven, Jesus himself being an Apostle, Hebrews 3:1.

Thomas would have been numbered with the rest of us who receive the testimony of the apostolic witnesses, and who are especially blessed (having not seen, but believed).

But he did not rise to that, so he required a special visitation (apostolic in significance) and he thus takes his place as a seeing witness, not an unseeing receiver of apostolic testimony, which is our privilege, if we so believe.

I wanted to cite a reference to what I have just written but I cannot find one, so it remains my own observation of the facts on record.

It would seem to me that the reason the disciples were meeting on the Sunday is that it is the third day after the crucifixion and a Jewish holiday called coincidently enough the "The Feast of First Fruits". This is a picture of Christ as the first fruits 1Co_15:20 of those risen from the dead and is symbolized by the priest waving the sheaf in the presence of the congregation as Christ was displayed risen to the congregation. You have Passover followed by the 7 days of unleavened bread in which they would have met every day. I also agree with another poster in that the eighth day is a metaphor for a new beginning and could refer to the time period following the 7th day/millennium. In either case I think it was a Sunday.

It is also dangerous in my opinion to rely upon a translation especially of a dead language and be dogmatic about a definition. It seems to me that the word "meta" in this case has many shades of meaning including "among" and "within". As examples I will cite Mat_1:23, Mat_9:15, Mat_18:23, Mar_14:62, Luk_1:58, Luk_1:72, Luk_9:39, Luk_17:20, Luk_22:37 as alternate meanings.

The point being context is king and you would want to translate with the local context of the passage and within the context of the gospels. It is the method of the atheist who wants to translate a passage which would create a contradiction when an alternative definition doesn't create one.

An example of this is Mar_8:31 where this word is translated "after" when the scriptures plainly tell us that Christ would be raised ON the 3rd day, not AFTER the 3rd day. So by translating the word "during' would have not caused a contradiction.

So applying the prevalent definition which is with/within/among to this passage would render the eighth day Sunday. I would translate it: Joh 20:26  So afterward, eight days, again his disciples were within, and Thomas with them: then came Jesus, the doors being shut, and stood in the midst, and said, Peace be unto you. 

Meaning on the eighth day.