Motion sensor fogger
I am just wondering if there a way to attach a motion sensor rated for 2.5 amps to a fog machine that requires 4 amps?

Yes. Use the normally-open (NO) contact of a suitably rated relay (paying attention to whether the fogger is AC or DC rated). The contacts must be rated for the voltage and current being switched. The coil should be rated for the voltage output by the motion sensor.

I’d like to replace the manual switch on the fogger with the motion sensor.

That should be fine.

At this point if I just hook it up as is the sensor will trigger the fogger but then gets stuck in the on position and will not shut off.

Without details of the internals of your motion sensor and fogger any answer will be a guess.

I assume it’s because the fogger is drawing too much and won’t allow closure for whatever reason.

In electrical circuits &quot;closure&quot; means conducting. Your problem is that the switch won't open. Again, no details.