There's a few parts:
§97.109 Station control. (d) When a station is being automatically controlled, the control operator need not be at the control point. Only stations specifically designated elsewhere in this part may be automatically controlled. Automatic control must cease upon notification by a District Director that the station is transmitting improperly or causing harmful interference to other stations. Automatic control must not be resumed without prior approval of the District Director.
§97.113 Prohibited transmissions. (d) No amateur station, except an auxiliary, repeater, or space station, may automatically retransmit the radio signals of other amateur station.
§97.213 Telecommand of an amateur station.
An amateur station on or within 50 km of the Earth's surface may be
under telecommand where:
(a) There is a radio or wireline control link between the control
point and the station sufficient for the control operator to perform
his/her duties. If radio, the control link must use an auxiliary
station. A control link using a fiber optic cable or another
telecommunication service is considered wireline.
(b) Provisions are incorporated to limit transmission by the station
to a period of no more than 3 minutes in the event of malfunction in
the control link.
(c) The station is protected against making, willfully or negligently,
(d) A photocopy of the station license and a label with the name,
address, and telephone number of the station licensee and at least one
designated control operator is posted in a conspicuous place at the
Beacons have their own rules, which are too numerous to just copy/paste. The section is entitled §97.203 Beacon station., and can be found at ARRL.