In the 1973 WTT, for example, when mullingar - Athlone was still fully functional, the Galway mails were as follows:
Down Day Mail
08:20 ex Connolly
09:29 - 09:36 Mullingar
11:30 Galway
Down night Mail
Pearse 20:05
Connolly d 20:15
Mullingar 21:24 - 21:31
Galway 23:34
No up day mail working
Up Night Mail
Galway d. 20:15
Mullingar 23:32 - 23:45
Connolly 01:00 next morning
Pearse 01:30
The Sligo services were:
Down Day Mail
Connolly 09:05
Mullingar 10:22 - 10:26 Described leaving Dublin as "Passenger", but leaving Mullingar as "PAS MAIL"; they possibly switched the bags from the earlier Galway Mail here? Or, it left Dublin with the mail?
Sligo 12:40
Down Night Mail
Leaves Mullingar as a connection off the Galway at 23:40
Sligo 02:05 next morning
No Up Day Mail
Up Night Mail
Sligo 20:25 (This is the one I travelled on several times, in all cases with a pair of 121s up front).
Mullingar 23:21
Await Galway train. Returns to Sligo at 23:40 as above.
So - in summary - the morning ones went through, possibly; the evening one was a Galway - Dublin one, and a Sligo - Mullingar one.