I have replaced the battery with a light one. When switching the power on I have brief flashes on the screen.
If the golf trolley display is flashing constantly then this will most likely be the battery is too low on charge, but this sounds like a power connection problem. It won’t be the new battery as long as your battery is 12volts. The smaller sized battery you refer to will be the Ah. This is only the capacity i.e. how long it can run for.
I would look at the golf trolley battery lead connector it may be worn or slightly broken especially at the metal connection holes. Inside the round connector there are metal round connections these can get dirty, worn / Stretched and broken. If these connections in the round connector are not making a good contact then this will cause the golf trolley not to get a clean power feed from the battery.