O.K.,

Now, I'm not an engineering expert, but I have witnessed quite a few of these conversion installations of the "Mini-Starters" into these older applications over the decades of being in business, and the variations on the theme can prove quite interesting. Yours is the most common "wrong way to do it" and yes it most often will work, sorta.

The proper wiring procedure is to have a live voltage cable of sufficient ampere load capability that runs from the battery positive terminal directly to the starter solenoid's "BAT" terminal (the bigger stud & nut

). Now in actual execution practice this cable is most often attached to the "BAT" side of the fenderwell mounted solenoid and the normal "battery" cable finishes the circuit. But should not be wired thru or switched by the fenderwell mounted solenoid; as first it is unnecessary complication and the additional switching garners greater resistance hence lesser cranking performance from the motor.
B.T.W. We have noted that many of the currently available examples of these "old-style" fenderwell solenoids are not manufactured ('off-shore-shyt'!

) or capable of carrying sufficient amperes as the old original examples. Also the solenoids for use with the mini-starters were diode protected. This do to as for example, when the starter motor is powered and engaged into the flex-plate turning the engine over the electrical surge is in one direction, but the moment the engine fires, even with the shaft clutch, the shaft of the starter experiences loss of turning resistance and even a driving force that accelerates it, and this along with the inertia of the already spinning motor and related componentry, then the power is cut from the switch (this as one releases the key from the 'Crank' position moving to the 'Run' position), there is the potential for a power reversal with the spinning armature which now acting as generator sends an electrical value back up the cable; and this in the E.F.I. vehicles was found to be potential damaging to the E.C.U.'s.
Then for the 12V "SWITCH" terminal on the starters' solenoid (the smaller stud & nut

) should be routed to ignition/start/crank switching, which in typical retrofits such as these is to the fenderwell mounted solenoids' original starter lead lug/stud (which otherwise now is abandoned). This involves the least sum of re-wiring though in other fitments routing to a true "Start/Crank" switch may be preferred.

But this is not to be "jumped" to the battery/starter feed cable! First concern with hitting both terminals simultaneously is the timing event of the rate to energize the intended as separate circuits of different deliveries, that of the solenoid and its' resultant function vs. energizing the field and armature of the motor and it's resultant function. Next, would be that which was described previously of the voltage production after the key is released from the "Start" position; as if the solenoid is "jumped" to the "BAT" terminal then the potential voltage output supplied can keep the solenoid engaged and the starter gear engaged/stuck in the flex-plate, with the motor continuing to produce voltage that continues to keep the solenoid locked in place, no matter what one does with the key switch!

And, although some may not have experienced this failure, it does happen, even after its' been working fine for a duration, but one day............

"Racers have been doing this for years."
And this reminds of the GM "one-wire" alternators as racers have been using for decades; although practiced, and it also "sorta" works, these really aren't intended as a "one-wire" alternator!

Scott.