Par Car stops running after 30mins

[Tango Bingo]

Have a Par Car bought used and am guessing it's at least 10yrs old. 36V battery system with brand new batteries and charger is a Lestronic II type. Recently, have noticed the charger amperage does NOT lower and shut off automatically as it did previously.

Other main problem I am having is that the golf cart runs fine for 30mins or so, but then dies. About 20-30 minutes later, it is able to be used again. Have read several forums with similar topic which indicates issue might be the SOLENOID. It appears I have two solenoids vice a single one. Other forum and website I have seen only discuss one single solenoid. The cart when it runs is not particularly fast, so am also wondering if the two solenoids provide two speeds.

Wondering if the solenoid would also explain the recent problem with charging that I am also experiencing (e.g. the automatic shut off never happens, and the amperage does not lower even after a couple of hours on charge).

Would like to understand how to best troubleshoot the two solenoids. I have a multimeter. Thank you!