Is there any simple way to tell the tuning in the meantime?
Easiest way is to post a few sound samples.
But you can compare the doh button/tonic on each row of the Pancotti with a known note on another one of your boxes, or other reference tone. If you have a C#/D or B/C box then you have all the referece tones you need. So find the Pancotti's doh (probably the 3rd but sometimes 4th button from the chin - whichever starts the major diatonic scale on the row) and play it on the push. Then go to your 'reference box' and see if you can match the note. When you have a positive match, you're done!
You can also do it with the basses. If the Pancotti is tuned in one of the 4th-apart systems (G/C, C/F, A/D, etc.), then the second button from the top on the outer row of basses will likely correspond with the tonic on the outer row of treble buttons. On an 8-bass model, the 4th button from the top on the outer row of basses will usually correspond with the tonic key on the inner row of treble buttons.
Your box has 12 basses which throws something of a wrench in the works.. could have been a custom tuning or have basses in different places. Also, it's possible that reference tones won't match up very well if the box is either badly out of tune or tuned flat in the old stadard (A=435) or something like that.
Nice box, by the way. I'm jealous - it is positively gorgeous! Keep us posted.
edit : Great name for an accordion, too -- our cat's name is "Sandwich" and we call him "Pancotti." It's a long story but he really acts the part.
