Good Morning! What are the set of black 3/4ish rubber hose connections going to and fro on the passenger's side firewall near the top of the engine compartment of my 2001 Toyota Tacoma?

 

They are the hoses going to/from the heater core in the dash panel. Passenger side. Heats the cabin.
The one that comes from the small, black, square valve on the firewall, is going into the core, the other comes from, returning the cool, used water to the engine.

If they are "sputtering coolant" you have a pin hole leak someplace, in either a hose, one of them, or the barbs from heater core that go through the firewall. Be aware that those barbs are VERY thin metal. Very easy to bend.

If you go to pull the hoses off, and they've been on there for a long time, get a couple of new hoses, and cut the old ones off. Make a slit in the rubber, along the barb, without touching the metal, and peel them off. Peel the hose open carefully, and it will come right off. When you go to put the new one on, a little vaseline at the beginning of the barb will let the new hose slip on easily. Use the original hose clamps if at all possible. They actually seal better than the screw down kind. If you have to use the screw down type, don't tighten them too much. Juuusssst enough to snug the hose onto the barb, don't crank them down so hard that the start to shred the rubber of the hose, or bend the metal of the barb.

Good fortune to you!
Pat☺

 

Aloha and Mahalos! Appreciate the assist! Located the tear and replaced the black hose on the driver side of the control valve...that must be the return hose? Also, flushed out the control valve and exercised the ball valve. Needed to quick repair the one hose for my daughter's ride probably look into ebay or amazon if they sell sets of hoses. Is their a good tutorial to just cap off these heater hoses for a 2001 Tacoma? Btw, where do istart to troubleshoot my crapped out stock radio...which fuse/fusebox is assocuated to it? Thanks again!

 

The black hose entering the control valve on the driver's side of the valve? That is the source of hot water from the engine. The valve controls the hot water entering the heater core. The water flows into the heater core from the control valve, and exits the heater and goes straight back to the engine.
To not use the heater at all, simply couple the two hoses that enter the fire wall together with a coupler of some sort. Most auto parts stores carry them. The hoses are very inexpensive from the nearest dealership, available on-line. Since they are pre-formed, it's easiest to get them from a Toyota parts source. If you just want to couple the heater hoses together, I guess you could just get a couple feet of heater hose from any autoparts store, along with a coupler to hook them together. If you're going to do that, though, it would be best to connect the hoses coming INTO the valve, and out of the firewall. That way, you'll keep water flowing through the pipes, preventing corrosion build-up in the metal portions of the systems pipes.

I am pretty sure the fuse for your radio is in the cabin fuse box. There is a cover just above where the driver's left knee sits when he's sitting naturally. Use a standard screw driver, and pop the cover off. There are any number of pictures of what fuse is which available on-line. Just do a google for your year and style. Like search "2001 Toyota 4Runner SR5 cabin fuse box diagram", no quotes.
Just a note: there's probably just corrosion built up on a connecter or other. Check the contacts on the radio's connector, and work back to the fuse block. In your environment, corrosion is a huge problem. While you're at it, check the Battery terminals. I bet they're starting to corrode inside their connectors. Any connector you take apart, put a dab of Silicon Dielectric Grease in the female side before you re-connect them. It will help prevent corrosion. That includes spark plug connectors.

Keep an eye on your frame under the truck, as well. It will rust out before you can take a deep breath. Keep any rust cleaned off. DO NOT let it build up. Keep it coated with Rustoleum, fluid film, or SOMEthing that will preserve the metal. Including inside the frame rails.

Keep us up to date!
Pat☺

 

What coolant do you use ?