36769-05K is definitely a good number.
I have it listed in my 2005 SE parts book on page 42.
They call it a Secondary Clutch Actuator, repair kit ( chrome ) for the VRSCSE.
Looks like it comes with about 5 pieces including the seal.
I see that 36769-05K info also in the 2005 parts catalogs I have indicating that it
was a repair kit for the VRSCA and VRSCSE models (chrome) and that 36782-05K
was a repair kit for VRSCB models (polished). However, the dealer parts look-up don’t list either of these items as currently available so they are likely NLA but some dealers may have old stock.
A 36769-01KA, secondary clutch actuator repair kit ($61.40 MSRP, chrome), is still listed but appears to be marked “to be discontinued” and a 36782-04K, secondary clutch repair kit, polished ($155.40 MSRP). These repair kits appear to be for the older actuators with the 36759-01K bleed screws that seal with an o-ring.