Dublin pilot - Engine failure in IMC enroute for someone with an EIR or an IR or an IMC rating present exactly the exact same issues. It is an emergency and thus the pilot can legally do whatever they think is necessary. However, should a PPL or an EIR or an IR or an IMC rated pilot be flying in VMC over an extensive fog bank and the single engine fails then they are all faced with having to complete a forced landing in IMC with insturments that are in the process of running down due to lack of suction and limited battery life for the turn coordinator and pitot heat etc
So do you think that a basic PPL flying VFR on top or an EIR holder who at the same place and the same level has the engine problem you describe - which will be better equipped to descend through cloud and track a VOR/NDB and/or follow ATC vectors?
The circumstance I described was a developing situation, not an engine failure that had happened.
As for how an IR/IMC holder would deal with it vs a VFR on top/EIR pilot, well it's pretty simply.
An IR/IMC holder would divert to somewhere close by and perform an instrument arrival.
Neither a VFR on top pilot or EIR pilot would be trained to do such an arrival...hence why I don't see it as a good idea.
Speaking as someone who can legally fly VFR on top, I don't think very many people do, unless they have some instrument qualification. The dangers associated with being stuck on top, and your only way out being an instrument arrival that you are not trained for, are too serious.
I suppose an EIR course could include some instrument arrival training to cover this, but if it was enough to allow it to be done safely, then why not examine the student in it, and give them the privlidige?