Can I use the same mouse for both of my iMac?

You might be able to make it work with a USB mouse and a "KVM" switch. (One of the cheap ones that just does USB, instead of an expensive one that also does video switching.)

https://www.amazon.com/s?k=usb+kvm+switch

Here, I'm guessing that the USB mouse could be a "wireless" third-party mouse that is paired with a proprietary USB plug receiver. No Bluetooth mice (like the Magic Mouse) invited to this party, though.

Presumably you would want a USB keyboard, and a KVM switch with at least two USB ports for peripherals – so that you could switch both your keyboard and your mouse with the press of a switch or the touch of a button.

You can but it will be a hassle. You'd have to "forget" the mouse on Mac 1 and on Mac 2 pair it. Then repeat the process when moving back to Mac 1.

Better to get a cheap USB basic mouse and attach to one of them.