Steering Pulls left and right sparatically.

Try flipping the front tires right to left and so on car may have a radial pull road test to see if it goes right or strait (first check tire pressure )

Swap front tires and call it the day.

Could be air in system and right side not applying brakes. Also the internal rubber in brake line where solid metal line attaches to can deteriorate and form a blockage for brake fluid to not reach caliper on right side.

Could the front control arms be worn out and letting the differential shift around ?

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If if the steering pulls every few seconds of driving
the car,why are you driving it at all?

Driving 60 mph knowing you have a steering problem
is,to be kind -foolish & iresponsibe

You need to have the enire front end checked out
for worn & damaged parts,as well as the steering
rack

Doubt it is the pump.

Your car needs a front wheel alighnment.When it pulls under acceleration and then goes the other way,get an alighnment.Torque pulls the wheels one way and then the travelling pulls it the other.Hope this helps

It sounds like you have a bad balljoint or rack and pinion. Another possibility is upper strut bearings.

What is happening is there is too much play in the ball socket. It rocks one way on a left turn and another on a right turn. You did not indicate a 2 wheel drive or 4x4. Some of the strut towers have bearings on top. You should also check for missing metal around the strut tower.

If you have rack and pinion, the hydraulic rods can be bent. But I would go more with the Balljoints because a bad rack and pinion would affect steering effort but not change the tire alignment in both directions.

sound like it has a control valve seal problem internally in the steering box, assured that the linkage is good, this can be dangerous due to loss,or forced steering at any time...focus on replacing the box......GL....be safe

rack and pinion.......