While electrical, rather than electronics, I'll put this page in this section. It won't be a how-to repair it, just notes that there are ways to deal with it, with brief hints. If you're competent at repairing electrical equipment, you'll be able to work it out for yourself. If you can't, then you shouldn't be attempting it.
I bought this oil heater several years ago, and recently it's 24-hour timer started loudly ticking like at wants to star in a movie as a time bomb (long after any warranty period would have expired). It's an electro-mechanical timer, where mains power drives a motor around inside it.
Can it be repaired? I'm not going to try to repair the timer, itself. I doubt it would be reliably repairable. And while it's possible that you can get a replacement timer unit for it, I'm also not going to bother.
I used that feature very rarely, and I don't care for automatic on/off timers on high-current portable devices that may be a fire hazard (especially heaters). It's too easy to forget it's going to switch itself back on, later, and it can come on when you're not there. Not only wasting power, but potentially being a fire risk in a couple of ways:
Firstly, if it got moved, or something landed on it. Even though these kinds of heaters don't usually get as hot as other kinds, it can still get hot enough to set fire to some things, and we live in homes full of flammable plastic things.
Secondly, if you're not there watching appliances, equipment faults can cause fires in the appliance, itself, with nobody there to just switch off when they notice something going wrong.
You being there to deal with problems can be the difference between simply having a broken appliance to repair or dispose of, and your house burning down.
I'm far happier with countdown timers. The kind that you set how long the device will be on for, and it switches off at the end of the countdown and stays off. But this heater doesn't have one of them.
Killing the tick
Importantly with heaters, do not work on them until they're completely cold. And before using an oil heater after it's been tipped over, give it plenty of time for all the oil to settle back down into its usual position.
Undo the three screws by the wheels on the side where the electrical parts are. Carefully hinge the whole side with the electrical section up and off (there are metal tangs on it that poke through other parts of the chassis). Be aware that the top plate may pop off, too, and you'll have to figure out how to properly reassemble it, afterwards. And be very sure that you have fully reassembled it. If you can't put it back together properly, then you should dispose of it. Also, do not over-tighten screws during reassembly, doing so will just chew through the bodywork and things will come apart, later. A heater that's falling apart will be extremely dangerous.
On mine, there was a metal jumper between two pins on the back of the mains timer that carried mains power over from the timer's switching terminals to the timer's motor terminals that can be simply removed. Now the timer motor doesn't run, at all, but no other functions of the heater are changed. So no more ticking noises, and (other than the thermostat) you'll be in full control of whether its on or off. Just set the mode switch on the timer for the device to be always on (the timer has a three-position always-off, timer-controlled, and always-on mode switch).
I would label things to say that the timer is disabled, such as on the power cord just below the timer. Labels on something that get warm, such as the heater itself, are likely to come off.
If you really want a timer-controlled heater, then I suggest simply buying a timer that goes into the wall socket, and plugging the heater into that. But I'd only do that in a room with no possible fire hazards (concrete floor, brick walls, nothing anywhere near the heater—including anything that could fall over and not land near it). But, personally, I'll only use mains timers on things that are very low risks for fire hazards, such as night-lights.