Greg, call it the long way around, but if you could perhaps (an i get this would take a bit of time) tell us the continuity pattern of the new switch, in each position, and you machines model number, and rough age.
With this info, I will be able to tell you how to wire the new switch.
To do so, you will need to test the continuity of each possible combination of blades, for each position of the switch. at a glance, i make that out to be 15 combinations for each key position.
M-R
M-S
M-B
M-A
R-S
R-B
R-A
S-B
S-A
B-A
EARTH-M
EARTH-R
EARTH-S
EARTH-B
EARTH-A
I know this is allot of testing, but if you get really stuck, tell me the continuity of each of the above combinations (on/off, or close/open) foe each key position, then tell me the model of your mower, and i can tell you what to do.
Hopefully, you find an easier way, but I'm here as a backup if you need it!