The pre-engaged starters pull a little bit more current through the white/red ignition switch wire than the inertia ones .

It's good practice to use the old solenoid as a relay to protect the wiring in the loom - keep the red/white on the solenoid, and run a slightly thicker gauge down to the solenoid on the starter from the switched terminal.

Both starters were later versions with solenoid built in/on.  Car had solenoid attached to inner fender with feed from battery to hot post and then a shorter feed to the starter effectively making a splice block on the old solenoid.  When I took that out a year ago to swap motors I over looked that and rewired the solenoid back to where I thought it would be last week.  Tracked that out and the 1275 fired on first crank and settled in nicely.  Once I get the drum to disc conversions done I am back on the road.

Car is mostly a 76 with various bits of other years blended in.  Last count was at least four colors.  Hybrid is a polite description.

Post some pictures of the 998 starter and the 1275 starter. We can't tell which starters just by the engine size - at some point someone may have fitted a non-standard starter to either engine. Also identify how old the Mini is so we know whether it originally had a separate solenoid - sometimes when a solenoid fails, someone might have added a separate one..

Having trouble with wiring on the 1275 A+ i swapped in place of the 998.  Not exactly sure of model starter  it came with but looks like one with solenoid on it.  But it looks exactly like the one that was in the 998 which was wired with a fender mounted remote solenoid.  Cable to post and one white/red large female spade connector to it.  Not sure which diagram I should be looking at.  Car is a bit of a mash up at this point.