The most recent AOPA Pilot magazine chronicles how it recommended the FAA allow DPEs to perform exams while utilizing Basic Med ("Alleviating ‘illogical restrictions’," p. 12). This is great and much-needed! Is there a timeline during which the FAA will consider that recommendation? What is the progress on that issue? Are they actively considering that? When will they make a decision?
Currently there is no offered timeline set forth. This is an evolving topic with many aspects to consider. Watch the AOPA webpage, any updates will be posted there as they become available.
I suspect this would have to be on hold until the reg change allowing BasicMed pilots to act as required pilot crewmembers other than PIC is completed. Remember that examiners are by regulation not supposed to be PIC during a practical test.