We have the same tow set up. We added the 12v charge line from the MH, 7 pin to 6 pin on CVR. Then put in a 12 v fuse just before the line connected to the CVR battery. We don't pull a fuse and have never had a dead battery while towing. The Brake Buddy is plugged into the 12 volt receptacle on the CVR.
That said the 12 CRVs and early 13 models as well are known to have battery and charging issues. We had ours go dead at least 5 times last year, before Honda finally admitted there was a problem. Every time the car would sit for about 3 days, the battery was dead.
Check with your Honda dealer for campaign # L96. This changed the battery to a heavy duty 475cca, and changed the charging to over 13 volts, from the previous 12.2 volts.
Beverley and Ken
2006 Winnebago Outlook 29B E-450.
2012 Honda CR-V AWD
Blue Ox Aventa LX tow bar and Brake Buddy Vantage.