Subaru Legacy steering wobbles while accelerating?



I have a 1995 Subaru Legacy with about 130K on it. Lately it’s had a episodic wobble in the steering. Once in a while, usually when I am moving off a complete stop or travelling around a curve, my steering wheel will start wobbling in my hand. If I am travelling slow enough, I can feel the individual ‘wobbles’ as short pulls to the right towards the passenger side (and what I believe is the drive tire?). These ‘wobbles’ increase in frequency the faster I go, but cease completely when I take my foot off the accelerator. As long as I am gliding or braking, there is no wobble, but the minute I step on the gas even a little bit, the wobble returns.

If I continue driving in a straight line, the wobbles increase in frequency, but over time diminish in intensity until they seem to go away altogether.

I have found nothing that consistantly causes this wobble; it is episodic and shows up sometimes when I veer right or left, but not every time. However, if the vehicle is in the middle of a wobbling episode, taking my foot off the accelerator always gets it to stop (at least as long as I don’t step on the accelerator again.)

I don’t think the problem is in the axle or the brakes since coasting or braking stops the wobble instantly, but I am worried that there is something going on in the mecanism between the drive shaft and the wheel that is causing this episodic wobble. It seems to be becoming more vigorous and frequent. Is there anyone reading this who might have a suggestion as to what this might be?