As mentioned earlier, Senso's website now purports to show the boys' status. It looks like a dynamic tag that gives real time information.
(I rather fancy Mr Chai)
Everything in my bones told me this feature was not to be believed. So I monitored the status descriptions over a day and a half and nothing, absolutely nothing, changed. The "available" ones never became busy and the "busy" ones never became available.
I'm now beginning to suspect that "available" means they are on Senso's payroll and may even show up for work, while "busy" means they're busy working at another job elsewhere. Naturally, this would be true only as of the date the webpage was updated.