(info "(make) Chained Rules") says The second difference is that if 'make' _does_ create B in order to update something else, it deletes B later on after it is no longer needed. Therefore, an intermediate file which did not exist before 'make' also does not exist after 'make'. 'make' reports the deletion to you by printing a 'rm -f' command showing which file it is deleting.
I only saw an 'rm', not rm -f. So the documentation needs fixing. Also here, Ordinarily, a file cannot be intermediate if it is mentioned in the makefile as a target or prerequisite. However, you can explicitly mark a file as intermediate by listing it as a prerequisite of the special target '.INTERMEDIATE'. This takes effect even if the file is mentioned explicitly in some other way. be sure to say which of .INTERMEDIATE: %.qq *.qq bla.qq will work. Same for .PRECIOUS, .SECONDARY etc. Yes .PRECIOUS mentions the % form will work, but do mention all.