“Do cell phones leave a digital trace everywhere you go?”
They constantly ping the nearest cels towers.
So, yes.
Signalling Systems No. 7 (SS7) is the telephony signaling protocol that (among other things) provide for mobility and roaming in cellular communications.
The protocol dates from 1975, and is not encrypted or otherwise protected.
Using rudimentary tools that have been widely available prior to 2008, just about anyone can track a cell phone from virtually anywhere in the world.
Generally, it helps if you know the International Mobile Equipment Identity (IMEI) which is used on Global System for Mobile Communications (GSM) cellular networks or the Mobile Equipment Identifier (MEID) which is used on Code Division Multiple Access (CDMA) cellular networks.
Most mobile devices come with an IMEI and and MEID.
If you know the cell phone number you want to track, but don’t know either the IMEI or MEID, you can collect it via SS7.