NOTE: I am a noob at bash scripts and the awk command - please excuse any dumb mistakes I make.
I am unable to substitute shell variables into my awk pa
Could you please try following, haven't tested it because no clear samples but should work.
funcName="<${2}>:"
awk_result=$(awk -v FN="$funcName" 'index($0,FN){found=1} found; /^$/{found=""}' "$ofile")
rfile=search.txt
echo -e "$awk_result" > "$rfile"
Things fixed in OP's attempt:
awk variable name to awk_result.var=$(......your commands....) fixed it for awk_result variable.awk code fix, I have used index method which checks if value of variable FN is present in a line then make a FLAG(a variable TRUE) and make it false till line is empty as per OP's ask.