Place one or more (more demonstrative) pop-up target(s) via editor.

In init field of each of them add:
this setVariable ["nopop",true,true];

At this time you can have raised or lowered target with:
this animate ["terc",0] (raised); or this animate ["terc",1]; (lowered).
Choose to raise or lower target(s) (raised by default).

preview the mission
Situation of target(s) is stable (no more anim). They are lowered or raised as you chose.

Now, fired at a raised target. This will lower then raise it. Target is animated in its cycle even if nopop is true.

You can't randomize pops-up delay, like at a firing range. The situation is weird with several pop-up targets.

A poor solution is to counter-act the scripted raise of the target in applying a "hit" EH and then manage the sequence:
in init field of target(s):
this setVariable ["nopop",true,true];
this animate ["terc",1];
this setVariable ["nopop",true,true];
this addEventHandler ["hitpart", {

_this spawn {
  waituntil {(_this select 0 select 0) animationPhase "terc" ==1};
  waituntil {(_this select 0 select 0) animationPhase "terc" <1};
 (_this select 0 select 0) animate ["terc",1];

}}];
0 = this spawn {

while {true} do {
  waitUntil {_this animationPhase "terc" >0.5};
  sleep (4 + random 4);
  _this animate ["terc",0];
  waitUntil {_this animationPhase "terc" <0.5};
  sleep (1 + random 1);
  _this animate ["terc",1];
};

};

Note: The Arma's script targetP_Inf_F_Hitparts.sqf fails as the following loop is breaking (after 10000 iterations?):
scopeName "root";
....
if (!isNil "nopop") then
{

		if (nopop) then 
		{
			breakTo "root";	
		};

};
anyway, you could modify the last part of your script, to read:
if (!isNil "nopop") exitwith
{
if !(nopop) then {_target animate ["Terc", 0]};

};

_target animate ["Terc", 0]