When trying to start it, it clicks like there’s a bad starter solenoid. In the key is in the on position, if jumped, it starts on it’s own. Have changed the firewall solenoid. Have had it also not shut off when turning the key off. Could it be the ignition switch? Occasionally starts normally, but other times only clicks when turning the key, other times no sound. Battery has been checked.
I[f] the key is in the on position, if jumped, it starts on it's own.
So, it starts without touching the key? It does sound like the ignition switch has failed.
Do you have a tilt control steering wheel? If so try changing the tilt. Don’t remember what year, but at tilt all the way down in an f150, one side of the turn signals would not work. I have been through about another truck every couple of years, they threatened to get me a new one, I said I really don’t care, it was either a 94 or 04, but not sure which.
When the starter solenoid makes multiple clicks when you try to start the engine it means the starter isn’t getting enough power from the battery to run the starter. If the battery truly is okay then you either have bad cable connections to the battery or the main battery cable has internal wire corrosion.
The other issue could be due to a faulty ignition switch but you should verify that before you change it out. Since the starter will work in RUN position make sure the switch contacts are going to the correct switch position. It may just be out of adjustment.
Sounds like a bad ignition switch or the wiring/control circuitry between the IS and the firewall solenoid.
My Ford truck has one of those firewall starter selenoids, an older model than yours. I’ve had to replace it once I think. On mine anyway there are four terminals. One is for the main battery connection, often the alternator connects here too; one is for the switched main power to the starter motor; one is for the “start” control signal connection from the ignition switch; and the last is used to bypass a ballast resistor in the ignition circuit and provide a hot spark during cranking.
If you can locate the terminal on the SS for the ignition switch connection, then monitor it with a volt meter; that should only get battery voltage with the key in “start”. If it gets battery voltage at other times, there’s a problem with the “start” control signal from the ignition switch.