The 2000 was wrist mounted according to the manuals.
http://fallout.gamepedia.com/Pip-Boy_2000
"PIPBoy 2000 (hereafter called the PIPBoy), is a handy device that you wear on your wrist. It’s small, especially by today’s standards, and it will store a goodly amount of information for you. And using modern super-deluxe resolution graphics to boot! Use the buttons to select the various functions of the PIPBoy. Some of the function screens have text in the display window that can be selected as well. These text buttons will change brightness when you move the mouse over them."
"The PIPBoy (as it is commonly called) is a handy device that you wear on your wrist. It stores information automatically for you, like a personal secretary, and also includes a clock and calender function for keeping track of time."
ZAX: "{301}{}{"A RobCo 2000 PIP Boy is a Personal Information Processor, a personal data device developed by Vault-Tec designed to be worn on the wrist. It is designed to monitor the individual's health, provide a terrain-mapper via powerful satellite uplinks allowing it to map the topography of areas in the immediate vicinity as well as call up large map "blocks" of several hundred square miles. It also contains a five-minute video recorder, a buddy chat program, timer and alarm function, cabling extensions to motion sensors, and allows you to keep a log, store reading materials, and play simple games."}"