Iwo Jima was a island in the pacific that was important because it was large enough to have an airfield. Airfields allowed the United States to create bases, and push closer to Japan. As both Japan and the US knew this, the island was well defended, and became a long and bloody endeavor.

Communication lines are double strands of wires (almost exactly like modern speaker/sound system cables), connected to a telephone. Multiple telephones could be in each network, but the system isn't complex enough to have phone numbers; if one person talks, every else listens. Even with radios, ground wire communications are redundant, simple, and worked. Wires could have been placed in squad, platoon, company positions, at observation positions, or going to a position in the rear. If a wire or telephone broke, your grandfather would patrol out to fix it.

Cable is not light, and hundreds of meters of cable is absolutely not light. It comes in a spool, which spins and unwinds when you walk ahead. After the cable is in place, it needs to be connected and tested, all with the added complexity of being in combat.

Marine infantry battalions were organized with three rifle companies and a headquarters company. Inside of headquarters company is a communications platoon of a few dozen people. However, it's incorrect to assume that your grandfather would have stayed with the communications platoon, and that the communications platoon was a cohesive entity. They would have trained together, and then split to the various other parts of the battalion as augments to provide a rifle company the ability to create its own communications network.

If your grandfather's company was one of the first ashore, he would've gone with them. Perhaps not as the first guy to jump off the boat, but right afterwards. He'd have been equipped with a rifle, like everyone else, but probably a few less grenades, and a few more specialized tools like wire cutter and wire strippers.

Field Telephones are what he would've been dealing with a lot. Here's an account of an Army communication specialist in Europe. This soldier seems to be part of a larger unit, connecting headquarters elements directly. If your grandfather was one of the first Marines ashore in Iwo Jima, working in a company would be much faster paced, with less resources, and obviously much closer to, or at, the 'front'.