Minds might waver as boring people pray at this vigil (8,4)
I believe the answer is:
midnight mass
'people pray at this vigil' is the definition.
(midnight mass is a church service)
'minds might waver as boring' is the wordplay.
'waver' indicates anagramming the letters (I've seen 'wavering' mean this).
'boring' indicates putting letters inside (some letters must 'bore' a hole into other letters).
'minds'+'might'='mindsmight'
'mindsmight' is an anagram of 'midnightms'.
'midnightms' placed around 'as' is 'MIDNIGHT MASS'.
(Another definition for midnight mass that I've seen is " church service".)