Concatenate two behaviours

Sounds like you'll want to use both of these functions that you've made in the Update() loop of the MonoBehaviour. Then, just like you said, use something to switch back and fourth. Here's an example.

 float timer = 3.0f;
 float timeToMove = 3.0f;
 float timeToShoot = 1.0f;
 float shooting = false;
 
 void Update()
 {
     timer -= Time.deltaTime;
 
     if ( shooting )
     {
         Shooting();
 
         if ( timer <= 0 )
         {
             timer = timeToMove;
             shooting = false; // switch back to moving
         }
     }
     else
     {
         Moving();
 
         if ( timer <= 0 )
         {
             timer = timeToShoot;
             shooting = true; // switch back to shooting
         }
     }
 }
 
 void Moving()
 {
     // your moving function
 }
 
 void Shooting()
 {
     // your shooting function
 }

This is an example of what you can do with timers and it's done in C# but you can apply this knowledge to another approach and in js.