It was a no mans land only patrolled by border police by both sides. The skirmishes started when the Indians violated the truce and started patrolling Pakistan's controlled territory and captured Kanjarkot fort. At the end of the war the border was demarcated with Pakistan Army relinquishing the captured Indian territory to the Indians as per the arbitration court.
I can provide you with Indian sources, saying the contrary.
https://www.globalsecurity.org/military/world/war/rann-of-kutch.htm
In the spring of 1965, Pakistani tanks (received from the United States as part of its Military Assistance Program) entered the Rann of Kutch.
The memoirs of senior Pakistani officers later revealed that the deployment of this American-supplied armor had two objectives. The first was to entice Indian armor away from northern India, where an attack on Kashmir was planned for later in the year. The second objective was to see how strongly the United States would protest Pakistan's use of tanks it had provided, in clear violation of Pakistan's commitment. The United States did protest, but it was ignored.
The Indians became aware in January 1965 that Pakistani border police were patrolling below the Indian claim line. Pakistani patrolling south of Kanjarkot may have been going on for quite some time without the Indians knowing it. There was little doubt, however, that Pakistani occupation of Kanjarkot would have upset a long-standing status quo. When Indian patrols discovered that Pakistani posts had been established in area claimed by India, they accused Pakistan of aggression in the Rann of Kutch.
After India lodged a protest, it increased its own patrolling activity. In mid-February 1965, Pakistani forces dug themselves in around Kanjarkot, which may have been previously unoccupied, although President Ayub of Pakistan claimed that Pakistan had "long" occupied it. India moved large forces into the disputed territory during the months of January-April 1965, established forward military posts therein and carried out full-scale land, sea and air manoeuvers in its vicinity, thus forcibly demolishing the status quo. Both sides built up the forces available to them in the area, manned strong points, and shifted defense responsibility from border units to the army. The Indian response of occupying other posts near the frontier and, reportedly, building an airstrip nearby brought the latent crisis to a head.
During April 1965, a series of incidents has occurred with both sides blaming the other. The Pakistanis, enjoying a militarily superior position, moved forcefully against Indian outposts near the border fort of Kanjarkot and most recently staged a "preemptive" attack at Biar Bet, deeper within the disputed area. The Indians were mainly on the defensive but, according to Pakistan, had established outposts within undisputed Pakistani territory.
It was only on 08 April 1965 when the Indian forces attacked a Pakistan out-post at Ding in an endeavor to complete a military take over of the territory to present Pakistan with a fait accompli that the Pakistan forces went into action for the first time, and it was on 19 April 1965 after watching India's actions in the Rann of Kutch for three and a half months that Pakistan forces went into the disputed territory for the first time.
