That looks like a Wisconsin engine. I'd be tempted to pull the plug out, roll engine to TDC, then put a 50/50 mix of ATF and Acetone in the cylinder. Amount would vary, but like enough to puddle up where you can see it through the hole. Pu the plug back in and let it set for a day or so, then check it. You'll more than likely see it gone by then. Roll the engine over and see if it has compression. If not do it again and see what happens. I've unstuck more than several valves using this method.
The reason valves stick in these old air cooled engines is because a lot of people don't let them idle for a while and cool down. If you would happen to get things freed up and running, drain and flush the crankcase to get the mix out of there. Get some Marvel Mystery Oil and add suggested amount to gas and oil, it will lubricate the upper cylinder and valves. I use it in all of my 40's-50's era engines I have on garden tractors, etc. Good stuff and it works.
You'll probably have to dress the points in the Mag too and set gap.
Model number of engine should be stamped in the plate riveted to the flywheel shroud. Model number of Mag. should be stamped on its case too. Here is a link to an OEM service and parts manual for several models of the Wisconsin.
www.pittauto.com/customer/piauel/pdf/Wisconsin_AA_AB_AK.pdf in a pdf file It should include that engine. If the Mag would happen to need new points or condenser, use the OEM part number found in this online manual to look for them. I got a new set of both from our local Columbus Diesel Supply who is a dealer for Robyn/Wisconsin engines. I called them to check and see if they could get them and they actually had them in stock on the shelf. Not saying you'll have the same experience, but parts are readily available.
Those are great old engines if taken care of right.