Judging from your description, I presume that there is ZERO fan blower activity for anywhere from one to thirty minutes?
Hardpan has the idea -- since you state that there is no climate control (set the temperature by dialing-in a number of degrees), I presume that your temperature setting is some sort of sliding button/knob, that goes from cold on one end, to hot on the other, with varying warm/cool temps in between. I also presume that you set your fan blower speed with another button/knob, which has several speed selections marked, from slow to fast, or 1 to 4?
Assuming that my above comments are correct, the fan operation/speed is controlled by the fan speed selector switch, a relay somewhere along the fan motor wiring, and the fan blower motor itself -- pretty simple, actually.
As Hardpan noted, wiggle all of the connectors between the battery and the fan motor -- at the fan speed selector switch, at the relay, at the fan blower motor to see if you can induce the fan blower to start up/fail.
Has anyone used a volt meter to check that power is available at the fan blower motor, during the time period that the fan blower motor is refusing to start up? Same test with volt meter, but check the incoming power-side of the fan blower relay. Same test with volt meter (fan blower is refusing to start) and check the hot side of the fan blower speed selector switch.
intothegoodnight