The link below answers this question with an official KB article for 12.X & 13.X AWS BIG-IP VE instances:
https://support.f5.com/csp/article/K45728203
Also, this behavior is referenced as bug ID744740:
https://cdn.f5.com/product/bugtracker/ID744740.html
NOTE: The procedure in the above BUG ID link worked on my 14.1.2.6 AWS BIG-IP VE w/ the addition of the modify hostname command.
bash
tmsh modify /sys global-settings hostname big-ip-hostname
tmsh modify sys global-settings mgmt-dhcp disabled
tmsh modify sys global-settings mgmt-dhcp enabled
tmsh save sys config