From your current connection description, it appears that "T2" and "T3" will be the ends of the Split Run Windings. Notice that "T2" and "T3" are jumpered together - such as in a Series Connected fashion.
"T4" would be the end of the 2nd Split Run Winding (this Coil having ends labeled "T3" and "T4").
"T1" would be the end of the 1st Split Run Winding (ends labeled as "T1" and "T2").
"T5" looks to be the Aux. / Start Winding's end.
If all this is correct, then changing the Configuration from Series (High Line Voltage, or 240 VAC) to Parallel (Low Line Voltage, or 120 VAC) would be done via "T2" and "T3", as described below:
[*] Remove the Jumper between "T2" and "T3",
[*] Connect a suitable sized Jumper between "T1" and "T3",
[*] Connect a suitable sized Jumper between "T2" and "T4".
All other connections remain the same.
If you want to check the continuity of windings to find out which is which, that may be very helpful for connection determinations (now and in the future). You would be looking to find ends of each coil, and which coil is the Aux. / Start Winding (it will be in series with the Start Switch, and - if used, the Start Capacitor).
Again, this is just an observation, so maybe additional info from others should be taken into consideration first (if anyone sees problems with my posted data, please chime in).
P.S. Don't know what to say about the "P2" connection from the Reset Button!
Also, are you sure it's a 120/240 VAC Motor? Is this indicated (in whatever "remaining" text) on the Nameplate?