There is no NHRA rule requiring the switch on either side, just on the rear most panel of the car.

Quote:

General regulation
8:1 BATTERIES
All batteries must be securely mounted; must be of sufficient capacity to start vehicle at any time. Batteries may not be relocated into the driver or passenger compartments. Rear firewall of .024-inch steel or .032-inch aluminum (including package tray) required when battery is relocated in trunk. In lieu of rear firewall, battery may be located in a sealed .024-inch steel, .032-inch aluminum, or NHRA-accepted poly box. If sealed box is used in lieu of rear firewall, box may not be used to secure battery and must be vented outside of body. Relocated battery(s) must be fastened to frame or frame structure with a minimum of two 3/8-inch-diameter bolts. OEM located batteries without complete OEM hold-down hardware must be secured to OEM battery box/tray using the same 3/8-inch diameter bolt hold-down method described in previous sentence. (“J” hooks prohibited or must have open end welded shut.) Metal battery hold-down straps mandatory. Strapping tape prohibited. A maximum of two automobile batteries, or 150 pounds combined maximum weight (unless otherwise specified in Class Requirements), is permitted. Maximums may vary according to Class Requirements.

8:4 MASTER CUTOFF
Mandatory when battery is relocated, or as outlined in Class Requirements. An electrical power cutoff switch (one only) must be installed on the rearmost part of each vehicle and be easily accessible from outside the car body. This cutoff switch must be connected to the positive side of the electrical system and must stop all electrical functions including magneto ignition. The off position must be clearly indicated with the word “OFF.” If switch is “push/pull” type, “push” must be the action for shutting off the electrical system, “pull” to turn it on. Any rods or cables used to activate the switch must be minimum 1/8-inch diameter. Plastic or keyed switches prohibited. Switches and/or controls must be located behind rear wheels on rear-engine dragsters.




Most of the time the battery is located on the passenger side to help add a little pre-load on the Right rear tire. this can also be done with ladder bars, 4-link, cal-tracs, or good shocks.)