I think my switch may have some terminals backwards
Original or pattern 2 position (on/off) ignition switch will appear to have either three or four male spade terminals. However, as at least two terminals are made of a single "U" shape, any female spade terminals connected to these are effectively just connected together by the "U", the switch will not disconnect them in its 'off' position.
Brown/Blue being from the battery negative terminal and in the middle of the three different wires, I suspect it and the Brown/White are both connected to the same "U"?
Yes, if you want to be able to turn the lights on when the ignition is off.
However, if you want the ignition switch to turn everything off, swap the Brown/Blue wire to a terminal that is not connected to the same "U" as either of the other two wires. You will need to check but your photo says swap the positions of the Brown/Blue and White wires?
Btw, while your bike's harness is old, it is not original afaik; originally, those wires had what are known as "flag terminals" - the spades at right-angles to the wires; the connections and the back of the switch were covered by a rubber moulding (97-2262); the terminals in your photo would not fit in the moulding.
All the lights now work except for the oil pressure light.
The bulb/holder White wire is connected to the other White wires (White wires are (should be) 'hot' only when the ignition switch is in its 'on' position)? The bulb/holder White/Brown wire is connected only to the pressure switch in the front edge of the timing cover?
If yes to both the above questions and the bulb holder can be separated from the shade, swap in a working bulb from one of the other holders?
If a working bulb does not work in the oil pressure warning bulb holder, do you have a meter to check continuity through the wiring to the switch?
If all tests point to the switch being faulty, buying a new switch is not as straightforward as it should be ...
If you have the correct parts book for your bike, using the switch part number (60-2133) is unlikely to get you the correct switch - not because Triumph messed up but because of the current parts supply chain.
BSA (Triumph's parent until 1973) used two oil pressure switch threads - National Pipe Tapered only in early 1969, National Pipe Straight after that. So, unless your bike has had its timing cover changed for an early 69 one, it should have a NPS switch thread.
However, if you order by the 60-2133 in the 72 500 book, you will be supplied a NPT-thread switch ... order 60-3719 to be supplied a NPS-thread switch.
Whichever switch you order/receive, trial-fit in the cover using only fingers, because the timing cover is very thin and flimsy beside the switch,
very easy to crack which will then leak profusely ... Using only fingers, correct NPS thread switch should screw into the cover right up to the sealing washer; if it does not, work out why rather than using a wrench to force it.
Nevertheless, irrespective of how much care you use fitting a new switch, be aware they are generally poor quality, it is almost surprising if they last.
