First thing-
Post the Sears 917 number so we can look at a schematic and determine which engine you have.
Saying GT 3000 is about as helpful as saying Chevy.

All the switches are ON or OFF, so it seems you have a "flaky" clutch/brake switch.

It's likely your ammeter that is going negative, but that simply means the battery is discharging vs charging.

Thought I posted this last night but guess it never posted.

It's 917-275010.

Thanks,

Your statement about hearing a click and seeing the ammeter drop to the negative sort of indicates that the interlock circuit to starter solenoid is good and that the solenoid is actually operating, but the starter itself does not spin (it may be trying to spin).
What you are seeing on the ammeter is the electrical load of the starter solenoid being connected to the battery. The dropping of the ammeter like this has probably been happening each time you have started the engine in the past, but you never paid attention to it until you began having a "starting problem".
The fact that you work the brake pedal up and down until you finally get rotation and starting is also likely a red herring that does not need chasing. You would probably get the same results if you were repeatedly operating the key switch itself to the start position. Basically, interrupting the brake pedal switch is simply causing the starter solenoid to operate in cycles of on-off until the engine moves enough to make a spin up.
It sounds more to me like the battery may be losing some of its charge in storage periods, and initially is unable to jolt the engine into a quick spin. After a brief period of running to top off the battery charge, subsequent restarts seem like business as usual.
It might also be that the starter may be have become "sticky" to the point that it does not want to jump into action on the first cold start after having cooled to ambient temperature.
Testing for possible loss of battery charge can be done by trying a boost start using jumper cables and a known good car battery. If the engine spins up and starts well when using a boost start, but not on just the tractor battery......you will need to determine if this battery is "going out", or if some kind of parasitic drain is trying to discharge the battery while in storage.
If the engine still does not spin up normally with a boost, then you will need to clean each and every "connecting point" in the entire starting loop circuit to ensure that there is not a place where resistance is high until after the engine has run and warmed things up. This means that you follow the large battery cables from the battery to the points where these cables attach.
Disconnect the cables from the battery before working on this part of the testing/repair. Disconnect the negative cable first and reconnect it last when putting things back together.
You will need to actually remove the positive battery cable from the starter solenoid posts and look for corrosion or sings of a loose fitting nut. Do the same for the cable connecting the solenoid to the starter, check at solenoid and at the starter.
Then you need to check where the battery negative cable connects to the engine or frame to ensure no corrosion or loose fit exists.
Don't presume that just because the nut or bolt looks or feels tight that it is OK. Even if the nut or bolt appear sound and tight, loosen them anyhow because corrosion itself sometimes can "tighten" the fasteners physically but still kill conductivity. Breaking the fasteners loose and retightening usually restores conductivity (if there was a lack of).

Let's do a quick test-
Jumper the 2 large studs on the starter solenoid together.
Does it crank every time?
IF so, that indicates a bad solenoid or bad cable connections to the solenoid.

I have the same problem with mine and I was wondering if it could be the stater ( not starter ) as I've already replaced everything else and cleaned everything as well?

stator has to do strictly with charging, not starting. If you've already followed Mownie's advice above on verifying good start circuit connections, would next have the battery LOAD tested by qualified shop to eliminate it as a possible cause; after that, check per Bill Kapaun's note and concentrate on first starter solenoid, then starter itself.