Any problem that the transmission had would be significant if it manifest with just a driving test.
Are you a mechanic? Are you familiar with how it should sound, feel, shift, etc when it is in correct order?
There should be no noise, no trembling of the shift stick, easy engagment of each gear without undue pressure required to move into each gear. Each shift should feel about the same as the others. Is the clutch in good order so that the transmission can shift as it should? Did the previous owner know about overfilling one quart?
No noise, easy shift and 13 years old would TEND to confirm a good transmission. At 125k, my transmission was like new. Others failed much sooner.
Good luck
James