That's about the time it takes for the driver/regulator tube heater to warm up. Could be a marginal solder joint in the Zener string, for instance. That string is inactivated when the regulator triode starts functioning.
Another theory is a marginal connection that stabilizes with the expansion from heating. I feel that's less likely because most items take more than 30 seconds to achieve operating temperature.
How long has the amp been functioning before this occurred?