When your solar has your house batteries in acceptance, or Float stage of charging, you can hook the jumper cables back up to help fully recharge the Engine starting battery.
Once hooked up to the engine battery, the voltage will likely drop back down to the 13's as the less than fully charged engine battery gobbles up whatever the solar can make. Do not worry, just unhook the jumper cables when the sun gets lower.
A drive to town and back Might get the starter battery to 80%, but perhaps not, and perhaps not even close.
Starter batteries do not do well when left at sub 80% state of charge.
Also, when leaving the ignition on without the engine running, it can destroy the ignition coil. I've seen it more than once. A dead battery, replaced or jumped, and the vehicle will still not start because the ignition coil is fried. If you soon run into such a situation, a no start or a stall/no restart, number one suspect is the ignition coil.