dr bob

It needs to be rated for the motor current. Most of those mushroom button things are set up with small terminal assemblies on the back. Suitable for a control circuit but not anywhere close to what you need for a primary safety disconnect. A real magnetic starter may be in order, with a mushroom and a key control disconnect. Most lifts come with a safety crossbar at the top too, so the idea of poking the tops of the columns between the joists may or may not work, depending on the direction the joists run. Most are front-to-back so no way to install the safety bar or the channels for the balancing chains.

Be aware also that the columns need to tilt up into position, so the clearance needed for installation will be greater than the installed clearance they advertise. For a 24" square base under a 12" column that's 9' tall, that makes the roll radius almost 2" bigger than the column height. Make sure you take this ito account, since you are already squeezing fractions just to fit it in there assembled.