score:1
Looks like you want to use the Azerbaijan one. To find this, I went to Rome2Rio's page on Tbilisi to Baku. This then shows the train option with Azerbaijan Railways (ADDY)
Duration 12h 10m
Estimated Price $6 - $20 USD
Frequency Once daily
And links to the rail website showing movement of the trains.
However it notes that "Buy tickets at the station", indicating possibly it's not possible online currently for cross-border tickets.