I have a 1990 Toyota Celica with a manual transmission. Recently I have a wired problem. When I start driving the car and change the gear the parking break light turns on and stay on for while. Some times it turns off after a while and sometimes I need to push the break then it goes off. Can any one tell me what might be the cause? I don’t know if it is related but I changed the alternator recently. Thank you.
Have you checked your brake (or break) fluid level?
Jad’s suggestion regarding your brake fluid is valid and this is definitely the first thing to check. Most likely, your brake fluid level is low. If it is, be sure to use the type specified in your Owner’s Manual.
However, I found the comment about recently replacing the alternator to be interesting. When the parking brake/brake system warning light and the alternator warning light are illuminated at the same time, it usually indicates a failing alternator. Do you know whether your alternator warning light is still working? (You can find out by seeing if it illuminates briefly when the ignition is turned on.)
It is not unheard-of for a rebuilt alternator to be defective. So, if your alternator warning light is burned out, you might be not be aware that the alternator is already dying. This is something else to look into if your brake fluid level is normal.
Could be just a sticky parking brake. Look under the car to see if the cable is gunked up or stretched.
which type of brake lever do you have? the lever between the seats, or the pull, twist kind on the dash?
if its the lever between the seats, look for junk down there. pens, bottle caps, paper etc etc etc. & clean the junk out.
these can prevent the lever from falling down to the ‘home position’ which in turn can leave the light on. (or in your case, on sometimes, when it jiggles a little bit)
if you have the dash twist pull type, try pushing it in. does that help? these twist pull types usually get lazy and the spring on the back of them gets stretched out, letting them not retract by themselves. the remedy is to find a large thick rubber band and look under the dash. find where to attach the rubber band to, to ‘help’ the rod stay retracted.
I checked the break fluid level and it was low! I added some and the problem is solved:)Thanks guys.
Yes, you added brake fluid. Good. But, why would the reservoir be low? It will lower, a little, as the brakes wear. It will lower if there is a brake fluid leak. Have someone look at it. Be safe.
Glad you found the problem, but it really is spelled BRAKE. 
The other thing is that you really shouldn’t be losing brake fluid so keep an eye on it and if the level goes down again, get it checked out by a mechanic.
Brake fluid level lowered to the point where the light starts coming on intermittantly is a sign that it’s time to look at the brakes. As the pad material wears, the piston in the calipers’ cylinders becomes more distended and the space becomes filled with the fluid from the reservoir. As that happens, the fluid in the reservoir becomes lower and eventually the light starts coming on.
Check your brakes. Consider the light a warning indicator, which it’s designed to be. Just because adding fluid stopped the light does not mean that the true cause of the problem is corrected.
And have the pads/shoes checked for wear on all four wheels. I think that that year Celica has front disc brake pads and rear brake drums/shoes.
I took the car to Firestone Auto-care and they said that the brake system is in good condition and there is not any problem. But I will have them check it again next time that I am going to change the engine oil. Thanks.