forester2002s

If it's a vibration (rather than a visual wobble) coming from 'somewhere' in the rear of the car, then it could be the main drive-shaft vibrating under load. The centre bearing of the drive-shaft (located forward of the rear-diff) could be loose, or beginning to get loose.

I think that you are right to suspect the drive-shaft. The drive-shaft shouldn't be able to be moved by hand. It should be rigid, not soft - especially in the radial direction. A passenger in the back seat might be able to tell where the vibration originates.

What about the belt-tensioner? Is it behaving itself? And another possible suspect: the belt guide-shoe, above one of the pulleys? (only installed on manuals, I think)

Found this in a 2011 NASIOC forum: So it looks like the following Subarus use H1 low beam bulbs: 2004-2005 Impreza 2003-2004 Baja 2000 - 2003 Legacy

Single H4 bulb, with 2 filaments.

H1 bulb are single-beam. H4 bulbs are twin-beam High/Low.

One other, often overlooked, maintenance item: Change oil in rear-differential. First, check for oil leaking from the differential, especially from around the input-shaft, and from around the left and right output shafts. Ideally, the differential case should appear dry and not oily. If there is evidence of oil leakage, then the oil-level should be checked, and it's not much extra work to drain and replace the oil. However, if the diff-case is dry, with no apparent oil-leakage, you might be tempted to leave well-alone; but it's really not difficult to drain and change the oil. There should be 2 plugs on the the rear face of the diff. Use a 1/2"-square male driver to release the plugs. Always remove the top (filler) plug first, in case the plug is seized. On most Subarus, the rear diff takes about 1L of 75W-90 gear oil. The trick to filling the fresh oil, is to buy a cheap 'turkey baster' (squeezy-bulb type), and use that to get the fresh oil in through the upper fill-plug; fill until the oil reaches the bottom of the fill-plug. And you're done.

While you're at it, it would be a good idea to replace the fuel-filter (the black canister that one of the fuel-lines is connected to).

https://www.ultimatesubaru.org/forum/topic/145506-ej251-engine-weighs-119-kg-262-lbs/?do=findComment&comment=1222275

Agree on both points. Electric gremlins are difficult to corner and deal with. And there are multiple ground-points to worry about. My philosophy on grounds is that you can never have too many grounds (I'm not totally convinced that this is always true). So rather than chasing bad grounds, it might be quicker to just add grounds (in strategic places).

Is anything interfering with the clutch pedal? Carpet or mat for example?

I've replaced the brake-pads (front & rear) on my 2017 Forester. And with no problems. But my Forester has the old-style hand-brake lever - no electronic brake gizmos.

Oil change/flush might help?

I would be tempted to to try a thicker grade of oil (but still within the recommended range).

My first thought is the rear drive-shaft (prop-shaft) bearings. But these usually cause vibrations when transmitting torque, for instance when accelerating in AWD. Same goes for the wheel bearings and half-shaft bearings. So it is unlikely that you'd feel any vibrations in FWD, with no torque to the rear end. So that leaves the rear-diff. I wonder if the rubber mounting-bushings on the rear-diff are failing. With no torque on the rear-end (when in FWD), perhaps the rear-diff can move around a bit, and this may be felt as a 'vibration'. I dunno, this is just my best guess.