Surprised that nobody mentioned that leaving the key turned on for long enough to drain the battery will in all probability burn up the points in the ignition. Burnt points won't stop the engine from cranking, it will stop the engine from starting. Been there, done that.
I would make a guess that your solenoid is bad and/or the battery is weak.
Do you have a battery tester, in lieu of a volt meter. There are two ways to test a battery. 1. with a hydrometer, a fully charged 6v battery should be 11.25 in each cell as I recall. (Going by memory here.)
.2. A battery voltage tester will test for voltage, then when you switch to the Load Side, it will show the actual available power in the battery.. If the voltage is low the needle will drop to yellow or red.
If you go looking for a hydrometer the parts stores will look at you like you are nuts. Been there, done that. Amazon sells them.
I have a diesel motor home that has six, 6 v. batteries for "house power" running through an inverter to make 110 v. The chassis has two very large 12v batteries to start the engine and/or on-board generator.
I have to keep a close watch on my 6v. batteries, if the water is low in one battery cell, it will knock out all of the batteries beyond that battery. The six, 6v batteries in theory put out 36 v, however they are hooked up in a series, maybe it is parallel, can't remember which, so the end result is 12v with lots of amps.