For £7.99 one of these from Amazon https://www.amazon.co.uk/gp/product/B010A6WB0A/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1 needs 5V @ 15mA and GND, and outputs ASCII lines at 4,800 baud. It is a satnav-type module and uses the satnav satellites to output your position, but one of the lines it outputs is the current time (UTC)! (Other similar modules are available, it is a standardised protocol and they are intended to connect to a car dash camera to allow the camera to record your position.)

Unfortunately 5V is not on the EP serial connector but maybe if RTS was always high it could be used to power the unit!