The old model works great and is fully supported by modern versions of MacOS. I used mine until January, and it is still in my desk.
Here's something to try. With the old battery powered trackpad, make sure Bluetooth is turned on (on older systems you may have to turn on pairing mode as well). On the old trackpad press and hold the power button. Eventually the trackpad should enter pairing mode where the LED flashes. Keep holding the power button and it should successfully pair.
Note, if the trackpad is paired with another Mac and that Mac's bluetooth is turned on and within radio communication distance, the trackpad will not pair with a new machine. In that case, unpair the trackpad from the previous Mac or make sure that Mac's bluetooth is off when trying to pair with a new machine.
The pairing process with those old trackpads was pretty cumbersome, but once up and running, they were very reliable, at least for me.