I tend to believe that a pilot could fly a sim solo for instrument currency (if the sim is appropriately rated) and 2) a CFI (not II) could operate the sim for such purposes.
I'm reposting what I sent you via PM:
The regulations don't specifically require a signature from the instructor in order to log the approaches for currency. The regs just say:
(4) A flight simulator or approved flight training device may be used by a person to log instrument time, provided an authorized instructor is present during the simulated flight.
Since no training is involved, there is no real need for the person to be a -II, based solely on the regulation itself.
However, the old Part 61 FAQ's did interpret this as training and said "we write the rules and our interpretation is correct by definition", which sounds rather childish to me. Here's what they said:
QUESTION: Would a pilot using an approved flight simulator or flight training device to meet the instrument currency requirements of paragraph 61.57(c)(1) or (2) need to have an instructor present?
ANSWER: Ref. § 61.1(b)(10) and § 61.51(g)(4); Yes, if using a flight simulator (FS) or a flight training device (FTD), the instrument currency requirements must be accompanied and monitored by a:
1. Certificated Flight Instructor-Instrument (CFII) who is appropriately rated and qualified;
2. Instrument Ground Instructor (IGI);
3. Advanced Ground Instructor (AGI);
4. Part 142 training center instructor who is appropriately rated and qualified;
5. Persons cited in § 61.57(d)(2) and who are appropriately rated and qualified;
6. An ATP in accordance with § 61.167 and who is appropriately rated and qualified; and
7. An authorized instructor as defined in § 61.1(b)(2), and who is appropriately rated and qualified.
And for those of you who will argue that currency is not the same as training, the answer is still yes. We here in AFS-840 write the rules and we also write the policy and we say that currency is training. So, the answer is yes.
To use a FS or FTD you have to have an authorized instructor there to monitor the training.
So the FAA opinion, which really has no legal standing anymore, is that the instructor must be a -II. Note that still they didn't say there is a signature required, but as you know, CFI's are required to endorse logbooks for training. To know for sure would require a letter of interpretation from the General Counsel's office.