Hi again,
Ah, K2... the originally K6 supplied diag confused me.
A couple of points... with the non-OEM lights switch you have, and wired as it is, the rear light will always simply come on with ignition, it has to ... as I think you've connected the BROWN / WHITE to BLACK (as K6 diag shows). The K2 was not originally wired like this, the BROWN / WHITE was supplied 12v via the handlebar lights switch - which you seem to have done away with. No matter...
As you've wired it, the small Park light should come on too with ignition .... it seems there is a break somewhere in this BROWN circuit... the BROWN wire should exit the ignition switch and run to both the front Park light AND the Tail light, so check for continuity, connections, failed bulb and good earth.
Can I assume your IGN key switch is 'standard K2 Honda'?
Is the Brake light circuit working ok now?
In the top diag below is how your bike seems to be wired, and frankly, apart from the dicky Park light is as good as you'll get.... it it is correct and working 'as advertised'.
As you say, in the P2 position the Tail + Park should operate, but NOT the Inst illumination lights. When you say, 'No parking light with P2 yet", do you just mean the front small lamp, or both? Anyways, see the 2nd diagram & check against your bike.
So, your wiring seems about right barring the Park light glitch, but can be improved however, as I THINK your non-standard light switch can be better put to use.
Basically, it is likely a Centre OFF DPDT (double throw, double pole... YAWN) switch, and if so can be wired to only select the Tail / Park / Inst illum lamps at Headlamp ON, ie Low or High.
First though you need to check it is indeed a DPDT... ie get your meter & check... (see 3rd diag)
In Centre / OFF... there is no continuity between any connectors.
In Left position... A & C connect, B & D connect. (But A & B, or C & D, indeed all else remain isolated)
In Right Position A & E connect, B & F connect. (but A & B, or E & F, indeed all else remain isolated)
If all the above hold true, then you can wire this switch to provide 12v to the IGN switch BROWN / WHITE (instead of the BLACK) at Headlight ON.
Basically you'll join A to B, and D to F to BROWN / WHITE, whilst DISconnecting the BLACK to BROWN. This then will enable you to control the Rear / Park light via the Main Light switch as in the 3rd diagram. The P2 position should not be affected & continue to work as Honda intended.
Hope it all makes sense, good luck,
Simon.