Where can I download a schematic diagram for a Gemini XL-500?

Check motor bearings?

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Look at the cartridge make and model number fitted. Put that into Google and the type of stylus needed will show up.

how to fix a target switch on a gemini xl500ii

http://media.musicalplanet.com/pdf/GMN041.PDF

Here
http://www.stylusplus.co.uk/gemini-xl-500-mk-ii-record-player-stylus-8489-p.asp

This seems to be a pitch control issue. controller,
replacing \t,could be worn over time,
SL1200 Technics - if you want a solid long lasting excellence of sound reproduction for many years to come,

I had the same pitch control issue,
happened on one of my decks so I replaced the controller and good to go from there,

Another important tip -
never lubricate the controls sliders with any thing apart from the correct greases or oils applied by the manufactuer,most people dont think of the damage caused by the cleaners they use ,some aerosols eat away the fine oil that lubricates the pitch control sliders making them dry and brittle eventually cracking producing odd random performance issues,

hope this helps,cheers Misterdj

you need to replace the Pitch controls. I'm presuming it is a sliding pitch control. Use the Red start stop lights that reflect on the rotating wheel. put the pitch in center 0. does one row of the dots on the wheel stay completely still.now just turn it up op down a bit until it starts to move the dots slightly. now watch the dots now while there moving. Do they fluctuate they should be smoothe. do this on both decks to find out which one is fluctuating.

try replacing the drive belt with brand new one and see if this improves the situation

on top of the pitch control there is a small hole, in this hole you can use a small screw driver  and turn it left and right to free any dirt inside this is the master pitch control