Perhaps somebody has replaced the original switch with one from an earlier model, ie a 1-position one, although I find that hard to believe as I can't imagine the previous owner resorting to using the solenoid, or going to the trouble of fitting a separate starter button.
If the key no. is stamped on the barrel lock that would indicate an earlier one as the 95 & 110 models no longer had the number on the barrel lock for ign./boot, which previous models did, however, I've no idea whether replacement ones would have had numbers.
From memory, the original key numbers were on a plate affixed to the nearside A-post, which, if still there, might give you a little more info as to whether you have the correct keys/numbers, although, of course, lots of things might have happened over 60-years.
Eta: thinking about it, 95 & 110 might not have key number on the plate? Glovebox key should also open the boot: driver's door the ignition.