Looking for a sustaining pedal for the Casio ctk 401 keyboard. What models will be compatible?

No you can't as our PROPER Expert Cindy says.

Casio Ct-636 does not support any sustain pedals.Amazon.comhttps://www.amazon.com > ask > questions
A: Casio Ct-636 does not support any sustain pedals.

The other 'Contributor' probably saw this

CT-S1000V - SupportCasio https://support.casio.com > manualPDF

This Digital Keyboard does not come with a pedal unit. • You can use the PEDAL1 jack to connect an optional (SP-3, SP-20) sustain pedal. You can use the.

Generally, all Casio sustain pedals are compatible with all their keyboards, but i normally recomend the SP-20. SP 20 Pedals Products CASIO

Buy sustain pedal made for CASIO or switable model.
Pedal for Yamaha or Roland will work in reverse on a Casio.
If you cannot return for exchange, then open up and solder a different type of micro switch.

http://support.casio.com/manuallist.php?rgn=1&cid=008
The link i have attached is a direct to Casio's website and their user manuals. i dont think the one your looking for is on the however, you might find a model very similar to yours to use as a reference.
is there a problem your having with the keyboard?

The Yamaha FC-3 uses a TRS (three conductor plug). The PX330 does NOT use TRS jacks for the sustain and sostenuto pedals so they are NOT compatible with the Yamaha FC-3. Therefore I would conclude that continous sustain that the Yamaha pedal would be used for is NOT supported.

No it does not have a sustain pedal input an there is no way to add one, sorry.

Make sure you are plugging it into the place for the sustain pedal. If you happen to plug it into the audio out it may kill the sound.

The sustain pedals have only two wires. Usually they terminate in a 1/4 inch mono plug.

yamaha USUALLY sustains when switch is closed. Roland usually sustains on a switch between the wires when the switch is open.

NO POWER should be supplied BY the sustain pedal... it is ONLY a switch.

First, check your volume. Try turning it up the whole way. If that doesn't work, then try moving the slider switch to normal, and playing.
Also, try using the keyboard in Song Bank mode. If you have a Sustain Pedal, make sure it's in the accessory port and not the Headphone port. If none of this works, then you may have blown a speaker. Parts are cheap from Casio ($13.00) and are relatively easy to put in yourself.

Yep!!! Happens all the time and only a few synths have the option of selecting the operating mode.

NOW if you can open the pedal, USUALLY the switch has both the Normally Open and Normally Closed functions that a single wire can be moved to reverse the operation.

USUALLY you will need a soldering iron to make the change.