Hi hockeymark, welcome to Outdoorking.

Murray has all of its Illustrated Parts Lists posted on the internet, here:
http://partsandservice.com/html/Murray/lt/

Here is the one for the 42900A:
http://partsandservice.com/html/Murray/lt/lt42900a.html

I do not see any carburetor solenoid, or wiring for one. Note there are several red and several black wires, BTW.

Is this the correct wiring diagram for your ride-on? Is your engine a Briggs 287707, as shown in the parts list?