Which just adds another notch to the column saying bad ground or insufficient voltage.
And even though your 4-way issue might turn out to be a simple thing, there are a few things you should do first (or at least early on in the search) to make sure your wiring system is up to snuff.
Since it's a '70 your fuse panel is almost guaranteed to be a rusty mess. Even in the desert southwest they can't help but rust.
For all '66 to '70 Broncos, one of the first steps to take in making sure the electrical system is in good overall shape and that you don't chase your tail on each individual symptom, is to disconnect the battery, then unplug and clean the two rectangular firewall connectors just behind the engine where they pass through the firewall.
Clean and inspect for burns, melted wires, corrosion, etc.
While they're out, you might as well unscrew the fuse panel from the firewall as well. This way you can inspect for smashed/crimped/rusted wires and connections on the back.
If the fuses and contact clamps are not that badly corroded, you can clean them the best you can and reinsert the fuses. Reinstall everything carefully and then move on to the next phase.
If on the other hand they are very rusty (very common unfortunately) and won't clean up with a quick wire brushing, you might try this. With the fuse panel hanging there and accessible (relatively speaking that is) try to rig up a way to soak the whole thing in a container of Evap-O-Rust liquid. This is good stuff and will turn what's left of rusty metals into their basic selves again. If there is any left to work with that is.
Once that's done, apply some sort of anti-corrosion product and put the fuses back in. This might include dielectric grease, electric grease, or even some spray-on metal protectant that leaves a long-lasting film. Just make sure it's not super conductive if it's a spray. WD-40 is perfect for short term, but wears off/out pretty quickly. Not sure what else is out there, but the greases are good for this.
Now check your main battery negative cable. The main cable goes to the engine block of course, or the engine would not start reliably. But do you have an additional body ground? Ford used one, but most people that install a new battery cable leave that off. As the trucks age none too gracefully, this ground becomes even more important.
An additional 10ga wire from the battery to the base of the starter relay/solenoid is a good start.
Then add another one while you're at it, from the back of the intake manifold to the firewall. Ford never put these on Broncos for some reason, even though they put them on practically every other car and truck.
And NOW you can move on to finding out what's wrong with your flashers. It might have been fixed by all the other stuff, or it might be in your turn signal switch, or it might be a fault in the hazard switch on the dash. But at least you'll know it's not a bad ground, connector or fuse panel issue!
Oh, by the way...
You did check BOTH flashers when you were testing under the dash. Correct?
There is one for the turn signals and one for the hazards. Might be an issue with one or the other.
From the factory one is blue and one either white or metal. But they're on separate clips and often on opposite sides of the steering column. But they're there.
Maybe that's why they act like they're working when you flip the turn signal lever?
Good luck.
Paul