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Ah, I should have looked more closely at the docs to see if there was a public API for that before poking around in the package internals.
In that case, I suggest we change this bit in the test:
 # We look inside the context module to find out which
 # start methods we can check
 from multiprocessing.context import _concrete_contexts
to use the appropriate public API:
 # Need to know which start methods we should test
 import multiprocessing
 AVAILABLE_START_METHODS = set(multiprocessing.get_all_start_methods())
And then adjust the skip check to look in AVAILABLE_START_METHODS rather than _concrete_contexts.
I'll make that change tonight if nobody beats me to it.