The practical answer: stop only where parking and pedestrian access are clearly legal and safe. Water beside a road may be drainage, irrigation, wastewater, flood runoff, or a damaged pipe. Never assume it is suitable for touching, drinking, or bathing.
Why the old “follow the greenery” idea is unsafe
Green vegetation or running water does not verify public access, water quality, land ownership, or road safety. The Dead Sea and Jordan Valley corridors also include fast roads, unstable shoulders, extreme heat, sinkhole zones, military or agricultural land, and channels exposed to flash floods.
Five checks before stopping
Legal pull-off
Use a declared parking area or signed viewpoint. Do not stop on a narrow shoulder or where visibility is poor.
Declared access
Confirm that the site is public and open. A gap in a fence or an informal path is not permission.
Water identity
Do not drink, bathe, or wash with unidentified roadside water.
Weather and floods
Check heat and flash-flood warnings before entering any drainage channel or wadi area.
Return route
Make sure rejoining the road is legal and visible in both directions.

Better alternatives to an improvised roadside stop
Choose a signed viewpoint, regulated beach, reserve, service area, or town stop where parking and facilities are known. For the western Dead Sea corridor, Ein Bokek and Neve Zohar are the clearest visitor bases; Jericho or Beit She'an may fit northern Jordan Valley routes depending on the itinerary and current access.
Day trip or overnight?
An overnight stay is useful when the road day would otherwise combine long driving, desert heat, and several stops. Staying near Ein Bokek or Neve Zohar can reduce pressure to improvise beside the road. Jerusalem may still work as a city base for one confirmed Dead Sea destination.