Wow, It's been 20 years since I was playing with Smith gauges and back then Nisonger on Long Island was THE place selling them in the States. They got hit very hard by Hurricane Ian but their service/support arm is back up and running so you could give them a call - They were pretty helpful to me in the past.
Phone them @ (914) 381-3600
Weekdays, 8am - 4:30pm Eastern Time
Or
Via e-mail 24/7 at info@nisonger.com
What I remember from my Austin Healey days is that the gauge can is grounded as part of the light circuit - The gauge functions are grounded through their respective senders. The lamps have their own holder and + wire going to the lamps. The other gauges all had their respective sender going to the "T" terminal and +12 volts goes to the "B" terminal. Often, T was marked on the back of the can but not B, but that was for a single function gauge. T was always on the left on the back of the can, but I don't know where the other sender wires connect on your multi-gauge.
I found this info source on the web:
Triumph owner's club, New Zealand,
https://www.triumphclub.co.nz/...-gauges_Pt_1_1v3.pdf