I have a Precision trolley with a T handle. All lights come on. Using the controller, after turning it up, it will go for a bit then stop and restart again, and repeat the sequence. It also happens if I set the speed then just use the on off button. It also starts on its own sometimes.
When the golf trolley lights up and all the lights come on as normal but when using the speed knob control and turning it up or down and it scrolls ok. The golf trolley stops whether using the speed control or the automatic distance control normally would indicate a problem with the connections, the battery lead is the first place to look for connection looseness or dirt or broken connection. Occasionally a battery damage can cause issues like this, but with the trolley starting on its own this sounds more like either a controller box fault or a handle circuit fault. These are difficult to determine exactly where the faulty lies and is a process of elimination by replacing both parts.