It may be your settings, but even then SOMETHING should happen.
About the settings: in the Editing tab your will find some settings for the behavior of the fading, cross fading etc. If not, I suggest that you try the options a see what happens.
After you have dragged a transition into its place, you have some options to change the behavior too, click on modify and change the settings to see whether that makes a difference.
If not, then it would be good to tell us a bit more about your environment. Which version of PD, what kind of video files, what are the settings of your project, that kind of information.

Also did you try a transition in isolation, e.g. new project and just two video files? Still nothing happens?

It does not appear that there is any space between those two clips but spread out the timeline to double check. All it takes is a frame. HP Envy Phoenix/4thGen i7-4770(4@3.4GHz~turbo>3.9)
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Head scratching here . .
I'm using PD18, v18.0.2725.0 installed on 25 June 2020.
There's nothing in the settings that caught my attention, so I did a practice project with a photo and 2 video clips (same ones in the project that had the issue): put a transition between each one (pic-->clip, clip --> clip) and that worked OK. So, pulled the settings panel down, editing page and screenshotted both of these together (attached, image 1) FYI.

And since that worked OK, problem with the original project file so I went back to that project and the section that had the issue, and tried to do the same thing with it, again. And this time it worked. Screenshot (attached, image 2).

I've seen this sort of behaviour with other editors, but usually there is some other indication (eg v slow response to simple task like mouse movement) that there's knickers in a knot somewhere, and re-start of app might fix it. There was no such indication here before I posted the original query. Other than the transition apply did not work. On very limited experience with PD18 (3 weeks) 1st time I have seen it with this app.

??

Davidk101 - The Transition won't apply.jpg show the red arrow to place the transition below the video portion to the audio portion of the video clip. Others have reported the same behavior. The fix is simple. When this happens then move the mouse upward about 1/4 inch or more to see the box of the transition. Release the mouse button only when that transition is well in the video portion of the clip. That works for others that have created a screen recording showing this behavior.

Tomasc,
I drew the line to indicate where I had wanted the transition to be, ie between those 2 clips. Did not pay any attention to just where between the clips I had dragged it to, or later when illustrating the task intent. During the drag, did not see any transition icon over any part of the video clips, but for a short time (less than a second?? barely enuff to even register it was there) there was a box in text with duration.

And in the latter series of tests when the transition drag did work, same "unawareness level" - dragged and dropped the transition to where I wanted it, and it took, icon displayed.

So, if that's the criterion - release whilst mouse drag is "between" the clip video or anything eg picture in the top level of the track, not the audio component on the lower level: duly noted. Also note that the User Guide does not make this sort of distrinction between the video and audio level of a timeline track when dragging a transition into place.

One thing that can make it difficult to drop a transition is if the timeline scale is too wide and all the clips are tightly bunched together. That will limit the active area to just a few pixels, and may also result in the transition being applied to just the head or tail of a single clip, rather than across both.

The same is true if your default transition duration is very short (like 0.2 seconds), or if the vertical size of the video track is very small. As you noticed, on standard A/V clips the transition can only be applied to the video section (upper part of the clip), but as long as you have a reasonably good-sized target area it should simply be a matter of hovering the dragged transition in the right place and dropping it.