You are not alone! There have been continuing problems that with BCC and the symptom that you are describing has occurred with others that have the Wurth unit. Battery Control Center Noise
(Your problem is somewhat different since the solenoid doesn't just hum, it cycles back and forth and that is the click that you hear.)
There is some sort of NHSTA recall or repair on the unit but the NHSTA web site won't download the pdf. FR has dropped Wurth going forward. I am pretty familiar with all sorts of BCCs and I bet that they were attempting to lengthen the life of the isolation solenoid by reducing the current while it is energized so that is stays cool as these solenoids stay energized for days or months when connected to shore power and they are a definite failure part. However, seems that they slightly overdid it and often the low current will not engage the solenoid and it cycles like what you, and others with that BCC are experiencing.
Of course, when you turn something on in the coach the house battery voltage will drop and in many cases it will then decide that it doesn't want to connect the chassis battery and will simply stop trying...hence the click goes away.
Note that Wurth punted on the problem...and FR punted on Wurth a while ago. Their response is, by now pretty much BS since they have undoubtedly had multiple complaints with the same symptoms.
I don't think that this is a major problem when you are connected to shore power since the house batteries will be charging and the click is just the chassis battery coming on and off. However, if it is a continual problem I would call FR to see what they say, since there are a lot of BCC vendors but replacing one might be a little complicated since the BCC also connects to a lot of your accessories on the coach. It won't hurt anything but it really shouldn't keep doing this all the time. Seems that Wurth doesn't even list the part anymore on their main web site.