Like Chief Science Officer Spock, I too am finding it hard to get definitive info on a convective tail...I have seen NWS use the term in their statements...this one is from Dec. 21, 2003:

"ETA IS THE ODD MODEL OUT WITH ITS FCST OF KEEPING THE STREAMS SEPARATED. THE GFS IS EXTREMELY CONSISTENT AND IS IN GOOD AGREEMENT WITH THE UKMET AND CANADIAN MODELS. THEY ALL FCST SHRTWV ENERGY IN THE NRN AND SRN STREAMS TO BEGIN PHASING
DURG THE LATER HALF OF THE PD. HPC QPF IS VERY SIMILAR TO THE GFS
WITH THE EXCEPTION OF HIGHER QPF AMOUNTS ALONG THE CONVECTIVE TAIL OF THE COLD FRONT INTO AR AND LA."

Were I to make an 'educated guess' I would think the convective tail is the tail end of the "comma" seen in many low pressure systems...I'll try to find out a more definitive answer...