Teleplay, it's not about the timer.
Yes, I realize that, but have to thank you because after doing the timer search for prices, I bought that one for myself. I really didn't know they came with 3 timers in one unit, a handy thing.
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Here's a slight turn on your idea to think about. How about an alarm clock. Lift the receiver, dial the time you want the phone to ring (military time using 4 digit dialing), go to sleep and wake up to a C4A or B1A ringing. Lift the receiver to turn the ringer off. A night stand would be a lot cleaner over time than a kitchen counter top and I think an alarm clock would be a widely accepted use - getting power to the ringer, a ring generator, would be the hard part but those 12 VDC to 70V 20Hz PowerDsine ring generators
https://www.ebay.com/itm/New-2PCS-RINGING-GENERATOR-PCR-SIN03V12F20-C-Power-Dsine-3W-12VDC-TO-70V-20Hz/252566429110are very nice and I have used them to test ringers for years using 2 27A 12VDC batteries in 27A battery holders.
https://www.ebay.com/itm/538B-B933-12V-27A-Battery-5pcs-Set-28mAh-Toys-Door-Control-Car-Primary-Battery/2734616986452 batteries have lasted over a year testing ringers. So, doing the electronics to get the phone to work as an alarm clock would be difficult since the ring generators are out there ($20 for the dSine plus $1 for two batteries and $1 for the battery holder and that part is done). Any rotary phone housing with a ringer and dial would work. Don't need the network. Lot of 302 bases, B1A ringers, housings and handset parts out there so no need to destroy or re-purpose a working phone. All it takes is money, time and the electronics know how. I'd put one on my night stand.
Ideas are easy and cheap and fun to think up, it's the getting to the final result that I find the hard, time consuming and many times the costly part.
Now, I have 4 302 lamp phones (bought them that way and nicely restored them). How about a timer circuit that turns the lamp on, or off programmed by the dial. Of course, since the handset is fixed, turning the dial would be the only option so dial 1 for one hour on, 9 for 9 hours on and 0 for off. Or dial 0 to enter program mode and then 1 to 9 for the hours until the light comes on. Or dial 0 once for time to off, dial 0 twice for time before coming on and dial 0 three times to clear the programming.
Actually, a DTMF pad with the # and * would make programming a lamp or timer a lot easier and more versatile than a rotary dial.
Note: these thoughts above are theoretical and in no way responsible for the conversion and/or destruction of any telephone.