The only correct answer I can give you is "it doesn't work". Chromebug is geared towards Firefox and was only once made compatible with Thunderbird. For me personally even that version never worked.
As for alternatives, there is no really good alternative that will help. The only other existing tool is Venkman, which at least used to work for debugging back in the days of Thunderbird 3.1. I don't think this tool is still actively developed though.
There are efforts to make the Firefox Developer Tools debugger work with Thunderbird. This option would make use of the remote support which is currently used for Android/Firefox OS. You would have to enable the debugging server inside Thunderbird and can then use the Firefox debugger to connect to Thunderbird. This option doesn't yet work, but stay tuned.