"I was unable to locate the eastern trailhead via automobile, but was able to successfully locate the western trailhead (at an athletic field on West Point Road near the Branford Town Dock).
There's ample parking at both trailheads (I walked to the eastern one but still couldn’t give you driving directions), and the trail surface was smooth and dry.
This is a nice trail for walking and/or jogging, not suitable for biking though due to its shortness and a narrow suspension bridge intended primarily for pedestrian traffic. The original trolley bridge, which still stands, is very sturdy and can handle bikes, strollers, wheelchairs, etc.
Feel free to e-mail me for more details.