Most of the larger sites I've been involved in over the years albeit the same major contractor the timelapse camera has been supplied by the security/CCTV provider. Always been a DSLR in and enclosure and hardwired power supply.
Had one element - bridge install that they installed a battery powered and I think PV powered camera to a lamp post to capture the crane rigg, carriers wheel out the bridge to the lift position and the lift and install on the abutments.
Recently another client, there CCTV/Security comes around once a month to do some drone pictures I think FOC