confirm
starter is wired correctly.
No.
Firstly, be careful with terminology:-
. the starter
solenoid is the part in your photo;
. C1 and C2 are terminals on the starter
relay, should be bolted to the underside of the battery carrier.
Right post of starter solenoid goes to starter motor.
Left post of starter solenoid goes to -ve battery.
Given the way your photo shows the solenoid mounted, these wires are connected to the wrong solenoid terminals:-
. wire from battery -ve should be connected to the solenoid terminal furtherest from the starter, closest to the cylinder block;
. wire to the stud on the starter should be connected to the solenoid terminal closest to the starter.
Look more closely, you should find it is Brown/Blue.
As standard, this was/is connected to the same solenoid terminal as the thick cable from battery -ve. The terminal is illustrated and listed in the parts book - "Electric Starter Mechanism", pages 36/37, part #24, 60-4592. The terminal is drawn as flat in the parts book but it is L-shaped -
Klempf's British Parts. TERMINAL, SOLENOID
Then it is the other end of the Brown/Blue wire that should be connected to relay terminal C1.
The Purple/White wire should be between relay terminal C2 and the "upper larger spade connector on starter solenoid".
The "small spade on starter solenoid labeled IGN" is not used.
No thin Red wire (original 14-strand or new 28-strand) connected to battery +ve; only the thick starter return cable should be connected to battery +ve.
Improvements to consider if reliable electric starting is required
If the cables between battery -ve and solenoid, solenoid and starter, engine and battery +ve are about 5/16" o.d., it is likely they are original, require replacement because they were under-specified. I use cable known here as "196/0.40" - 196 strands, each strand 0.4 mm. o.d. Primarily, its total conductor cross-sectional area is 1 sq.in. (in comparison, the original 'thick' cables are approximately 5/8" sq.in.

) Also try for as many strands as possible, the cable will be more flexible.
If you retain the Boyer e.i., if it is using 6V coils, replace with
Tri-Spark 4V.
The standard starter relay supply - the Brown/Blue wire connected on the solenoid terminal to the thick cable from battery -ve - is unfused.

I replaced the Brown/Blue wire and solenoid connection with a new fused Brown/Blue wire from battery -ve to the relay C1 terminal.
Ime, the standard alternator could not keep the battery charged for reliable electric starting if the bike was ridden for any length of time at low rpm, especially with lights on. I fitted my T160 with the high output version of the 3 phase alternator.