This is slightly ambiguous...
Head has several meanings on boats and sailing ships. The usage that most all recognize describes a "2-holer" traditionally (and conveniently) located at the front of the ship. However, the word can also indicate top.
In this case, 'Head rope' could be a type of line that is attached to the top edge of the sail, but as these are fisherman I suspect that on a fishing boat it is the line running along the top of the net.¹
(Please note that the word rope is not usually used on a boat unless it has a specific name and usage: once it is brought onboard and put to use it is referred to as line.)
The full context of the quote:
In any case, there’s nothing more daft than taking note of references like these. If there are certain fishermen who come to lay their nets here, at night, and in the week, it’s owing more to the fact that the area is little frequented at those times. This wretched habit makes them think the place is theirs, and the unsuspecting soul who takes advantage of their head rope runs the risk they’ll sink his boat, and with gunfire, too.
If you read a little further...
He bottom-trawled his nets across this very stretch of sandbank, seizing on a surge, and once out on the open sea he pulled the catch on board.
The fisherman is fishing near the mouth of the channel, and hauls up his catch once out of it.
A valuable contribution and primary source from Peter Shor...From the original Spanish:
"Esta maldita costumbre los ha hecho sentirse dueños del lugar y el desprevenido que se monta sobre la relinga corre peligro de que le hundan el bote a tiros."
...which translates to "run along the head rope".
Apparently there are locals taking advantage of the fish trapped in the nets. It appears they are in small craft using the head rope to pull themselves along, thus "taking advantage"². If they are on the inside of the head rope they run the risk of being capsized when the trawler begins hauling in the catch. The fishermen keep shotguns on board to to repel them. It is mentioned that one of these kept a Purdey shotgun for this purpose.
Although Merriam Webster has it as obsolete, I still see ads for this type of line being advertised on the web. in fact, the the Spanish definitions from RAE are almost identical to Merriam Webster.² See DRAE, which reads:
f. Mar. Cada una de las cuerdas o sogas en que van colocados los plomos y corchos con que se calan y sostienen las redes en el agua.
f. Mar. Cabo con que se refuerzan las orillas de las velas.
It is RAE sense 1 that the author used in the original, because that is the sense that pertains to fishing nets not to sails.
In its June 2021 (last month!) update to its entry for head rope, the OED marks as obsolete only the two senses related to ① either of a pair of shrouds, or ② a line for hoisting a flag up the masthead. The two senses exactly corresponding to those for relinga in the RAE, the OED gives recent citations for. One is for the bolt-rope at the top of a sail. but the other is the top-rope running along a fishing net, which is the use here.
It notes cognates in Middle Dutch, Old Saxon, and Anglo-Norman:
Compare Middle Dutch hōvetreep principal rope of a tent (Dutch †hoofdreep large rope used on a gun carriage), Old Saxon hōvidrēp principal rope (apparently on a ship).
RAE says ralinga was originally taken from Dutch. The sense used with nets it notes postdates the term head-roping for the same, suggesting a back derivation.
Apparently this comes from a translation from Spanish. I had been assuming that the original contained the word aprovechar, which often has negative connotations. However, In this case it appears that the locals were using the head rope to maneuver their smaller boats, thus creating a drag on the line.
This supports the "run along the head rope" idea.
In my opinion, the translation is confusing and not very accurate.