I have been having issues with wired mice as well. My inclination is that it has something to do with power draw, though i'm able to see movement on the screen, but clicks aren't always registered.
FWIW I started with a wired logitech keyboard and mouse, and just swapped out for a wireless logitech keyboard/mouse combo yesterday. Both were autodetected/configured immediately and without issue.
So, most likely two things that coule be wrong are the mouse to USB dongle connection OR USB dongle to kernel. Linux has pretty good fundamental hardware detection these days, I'd be very surprised if your mouse wasn't automatically detected and configured. I'd recommend working through the mouse to USB dongle setup process provided by the manufacturer.
@Buddickson I'd suspect that is a software issue with the GUI of the version of Linux you're using (more likely) OR a problem with the mouse hardware (less likely). The power draw change between the mouse button being clicked or not clicked should be insignifigant. The easiest way to test the hardware is to place the mouse into a different computer.
I would recommend you plug in the USB device before turning on the pi-top.