Narrowing top end tick. When the cam tensioner is out, and the bolt loosened, should it be able to be moved back and forth?
What does "when the cam tensioner is out" mean? what is out of what? You'll need to be more specific. The entire unit is the tensioner. The plunger is a ...well... plunger. (aka "push bar")
Yes, when the bolt is loose the plunger can move back and forth inside the housing. When the housing is on the cylinder, you loosen the bolt at the proper point of crank rotation, the plunger pushes forward against an idler wheel tightening the chain. Then you lock the plunger there with the bolt.
If you mean the tensioner (housing and all) is in your hand, and the bolt is loose, the plunger doesn't move? Iin that case it is stuck. This happens. You'll need to remove the bolt completely, pull the plunger out of the housing. Inspect it for burrs and corrosion. Polish the shaft. It should move smoothly and with little effort other than overcoming the spring. There is a seal in the housing that will provide a little resistance. But the plunger should not be stuck or it won't do the job as indicated in my first paragraph.