You may be fine to simply anchor into the plaster if the shelves will not hold excessive weight.

You can get more weight bearing by using molly bolts tat pass all the way through the plaster.

Drilling 1/16 inch holes to locate the studs is about the most reliable way without expensive electronics.

A very common method in plaster is to add 1x lumber in a band that is anchored at the corners (there will be studs there) and then attach the closet rods and shelves to the 1x.

The shelves WILL be holding a lot of weight. The one long wall will have all the attachments, as there are no end walls to use. It will become the primary clothes closet.

After trying several stud finders and not finding them to work in my own house, I finally found a good one a few years back. Is there anything in a plaster wall that will throw that off?

If it becomes too hard to find the studs, we can go the route of adding that wood strip. Thanks for the idea. Would it be like a 1 x 4?

How do you not have end walls in a closet?
if you do not want to run everything end-to-end that is a different matter.

Expanded metal was used in inside corners in many plaster installations to limit cracking.

It will show as higher density that the plain plaster and read as a stud.
You can try measuring (studs should be every 16 inches, but may be closer on one end) and drilling small easily spackled holes.

It is a long skinny pantry, about 3 feet wide by about 8 feet long. At one narrow end is a window, and at the other, the door to enter the room. The window runs edge to edge. Hence: no end walls available for extra support. The clothes rod will run along the long wall. It will be a Rubbermaid or similar wire shelf system. I am looking at one that uses vertical support posts in front too, if I can find that one.

With sheetrock walls, you can usually use any electrical receptacle as a reference point since the box will typically be attached on one side or the other to a stud. Since you are dealing with plaster, the boxes may not necessarily all be attached to studs, but you could take off a receptacle faceplate and, if you can't see a stud, use a piece of wire to probe to either side around the opening...of course turning off the power before fiddling around with a wire by the box. If you don't have a receptacle on the wall in question, is it an inside wall where you can make such a determination from the other side of the wall? Lastly, you can always do the drilling approach and put the holes where a shelf will be so you don't have to worry about patching and re-painting.