There is indeed a 135 check that is good for SIC only. I flew King Airs and a 421 as PIC, and there was a 135 checked SIC. He did his checkride with the POI after one of my checks.
I don't think he logged his time as SIC. I didn't log any time as a King Air or piston twin SIC.
Some people have argued that if you are assigned as SIC per 135, you can log it. Especially if the company does not have the OP SPEC for autopilot-in lieu of SIC.
I don't think I would log Navajo SIC time.
The only times I have logged SIC time---
1. In a two pilot airplane where I was required to be there.
2. In a type-rating required airplane that could be flown single pilot, but the PIC did not have a single pilot type rating. In that case, I had to be there too.
Example--A Premier is a single pilot airplane as long as you have an RA-390 S type. If you have a RA-390 type (no S ), then you are required to fly with an SIC. It even spells it out in the Limitations section of the AFM.
Will your SIC Navajo job turn into a PIC job? If that is the case, I would not let time logging issues keep you from it (assuming it is a good deal).
The company may have you log some PIC time under part 91 for you to qualify for 135 PIC.