Hi greatbrit and

to the Club !
I do love a challenge !
As suggested the Light Blue "loose wire I found" in your first Photo,
is not a Triumph Trophy connector.
It is likely to be from an after market Intercom, Camera system,
Heated Gear, or some other communications device.
A clue for the answers about the other connectors, is your non standard
Yellow coloured Rear Suspension Unit coil spring !
The Black Plug with Yellow Insert and 4 Pins is the connector for the Rear Suspension Unit
( RSU ) Damping Motor. It would normally be connected on the left side of the bike,
where you have noticed the four pin socket adjacent to the bank of four Relays :

From there the wires would be routed across towards the centre of the bike,
and attached to a clip before running downwards to the RSU Damping Motor.
I can only assume that your replacement RSU is either not motorised,
or the Motor is non operational, and has been disconnected.
Just for information, that "Box" on the right of the bike, labelled "N)Touch" P/N 2057599"
is the Triumph Electronic Suspension ( TES )Control Module.
Cheers

