1991 Toyota Corolla Steering Wobble at Lower Speeds

Vehicle is Toyota Corolla Seca early 1990s AE92 model, 4AF-carby engine. Engine done about 260,000 Km. No collisions or major mechanical work for several years.
Problem: pronounced steering wheel wobble/shake at slower speeds which becomes less noticeable at higher speeds (above approx. 60 Km/hr or 40 miles/hr). The steering also pulls to the left side.
External observation of slow moving vehicle shows front wheels to be steady but body has slight wobble.
Recently, for the first time, power steering fluid was below dipstick marker, so replacement fluid was added to correct level.
One of the boots (LHS) on power steering gear housing to tie rod is also broken.
Front wheel alignment and tyre pressures and balancing are OK.
Front suspension to wheel components as well as coil springs seem to be OK. Both steering tie rod ends are firm and in good condition.
However, when the vehicle is raised so front tyres are off ground, there is a few mm of free-play on RHS wheel when checked for front to rear (sideways) movement of this tyre. There is no such free-play from LHS front wheel. Also there is no top to bottom wheel free-play on either front wheel. Closer inspection indicates this horizontal free-play on RHS front tyre seems to come from RHS tie rod to steering gear housing looseness.
Steering gear is firmly attached to vehicle body.
My guess is that it is a rack and pinion power steering gear fault. If I had to replace the steering gear, would I have to remove the engine?

Any help/insight/suggestions in relation to this problem will be greatly appreciated.