Yes, I have a unit with with 2 foot switches in it. One spins forward, other spins reverse. I do all my tapping in the drill press.
It did take me quite a few relays to build. When a foot switch is pressed, the relays close to configure the motor wires for the correct rotation, after the configuration is done the power is applied. I use the original switch on the front of the drill press for an extra 240 volt muffin fan to add cooling to the motor when I am doing a lot of stop-start work. Just a Delta 17 inch drill press from Spags years ago, configured for 240V. The relays were all in my giant "junk" ha ha area.