I’ve managed to get a mouse working in Body Count by changing the device type. In the RGUI, I went to Settings > Input and changed user 1 device type to MD Mouse.
I’ve had no luck with Gangster Town. Like you, if I set the input device to MS Light Phaser, the mouse buttons work but I can’t move the cursor.
As I’m not sure what I’m trying to map, I’m not sure the Linux Joystick Mapper will help.