Should I be concerned about the timezones in my custom whonix workstations (arch, ubuntu, kali)? Installation mediums always ask for my country code. I usually pick a random one. When building workstations, which country should I appear to be coming from to make my packets less identifiable?
Packets won't carry your local time information, application data will though.
You probably want to make your timezone UTC since this is the most "generic" timezone and the easiest to calculate your own local time from (since timezones are measured as offsets from UTC). Random timezones are probably counter productive, because some timezones will have relatively few users and that's likely to just make you stand out.
Tails currently uses UTC for this reason, see their FAQ.