only if you are mechanically minded
I have never had a need to pull a 300 apart, but have fixed other mechanical/electrical timers.
Most of the time the motor drives the gears that cause the dials on the front to move, and also turns a hidden in the back gear with notch, or gear with trip cog on it to contact an electrical limit switch. When the limit switch (sometimes more than one) is contacted that shuts the motor off, closes the time out switch, etc. In your case it sounds like there is a literal screw loose somewhere. Look what the cog/notch etc is lined up with as it apporaches zero/60 You may find that the shut off switch has fallen off of its mounting bracket in shipping it to you. .