This addon called Loom is exactly what you need.
It allows you to specify ranges and specific frames that you want to render or skip. It's even possible to render every nth frame.
The addon allows to render single frames, multiple frame ranges as well as subframes, either directly within Blender's UI (as usual) or in a new terminal instance as background ...
The problem was that you used object coordinates. Object coordinates always point towards obeject X, Y and Z-axis. To fix this you have to either change it to UV or Generated coordinates which bend with the object.
SET TO GENERATED:
SET TO UV:
There are many ways to do it.
One of them: enable the "Copy attributes" addon in the preferences menu.
Set the 3D cursor in the spot you want as pivot point.
Create an empty in the 3d cursor loc.
Select the empty, shift select the cylinder, press Ctrl C "Copy Rot".
Set the arrow child of the empty.
Animate the empty (in my example on its ...
One workaround could be to animate the collection/scene visibility so in the frames you don't need the render, you set up everything to be not rendered (you'll get black images).
You'll have a very quick render for empty black frames.
Here's a reference:
I faced a similar problem with hair particles, and I've figured out how to solve finally. There was no way to delete cache or recalculate for me, I've tried any solution in various blogs. The trick for me was to set the start/end frames and then duplicate particle system and delete old, this operation forced blender to throw away any issue connected to the &...
EDIT: I guess the comment by @Gorgious is what you're experiencing. If not, try this solution:
If you've enabled the option Only Show Errors in the View menu of the Timeline window, than your keyframes will not show up unless there is an error.
It seems to be related to to Keying Set ... see Blender Manual.
Try to delete under Scene Properties > Keying Sets > Keying Set (if accidentally created)
or clean under Timeline editor > Keying menu > Active Keying Set slot
... if not your case provide more info as Chris suggested.
Some useful links ...
What is a keying set and how does it fit ...
If you add a Value Node to your graph, you can type #frame in the value field which will make the value correspond with the current frame as the frame changes. You could combine this with math nodes to set the timing and the direction (toward beginning or toward end) of the fade that you want. This example fades the background from bright white (At frame 0) ...
Figured out how to mirror the same animation keyframes to the other bone hand, without any re-work or manual labor required.
With the animated hand's bone rig selected, select all the keyframes in the Timeline (Shift+F12 to get the Timeline view and use your mouse to box-select them all or press Ctrl+A) and copying them with Ctrl+C.
Then proceeded to ...
Another possibility why you can't see the keyframes on the Timeline might be, if you've enabled the option Only Show Errors in the View menu of the Timeline window, than your keyframes will not show up unless there is an error.