Could someone help with an electrical question

[Kaellis 2]

I am working on a partial panel cockpit and just received an INOP autocontoller IIIB autopilot head unit. It has the two rocker switches on either side of the rotary roll control knob.

I want to use the switches to connect to my Arduino for the autopilot on/off and the heading activate switch.It’s easy enough to connect the momentary switch to the board. But what keeps the switches in the closed position, and the switch plunger pushed in, is a small 3/4” diameter electromagnet that holds the metal plate on the top back of the rocker. I’ve been able to energize the coils and get the magnets to hold the switch closed using two 9v batteries in parallel. I checked the resistance through the windings at 148 ohms. 
So my question…

Is there a better way to energize these coils and the electromagnets? Could I use a power supply?  If so, what might be the correct voltage and current to run through these windings without burning them up? How would I figure this out?