Do I need a dehumidifier that is effectively always working whenever it is turned on, vs my current one which is capable of being on without working?

Yes. The Inkbird controller is just a basic switch hooked up to a thermometer/hygrometer. It senses the input, determines if the temp/humidity threshold has been crossed, and turns off or on depending on the current rule. It doesn't know anything about the device you have plugged into it. Even the fact that the device you have plugged in will somehow affect the input data is implied. Some people turn on exhaust fans with their hygrometer-based switch as pulling in ambient air will usually dehumidify your controlled environment (think grow rooms).

The dumber you make the device on the other side of the switched outlet the less trouble you're going to run into. Here's what I use.

This is for you as well u/rachman77

This the fridge I ordered from Home Depot, which they kindly dropped off at my apartment;

https://www.homedepot.com/p/Magic-Chef-4-4-cu-ft-Mini-Fridge-with-Freezerless-Design-in-Stainless-Steel-HMAR440ST/207169805

I went with this model as it's all interior and no freezer. Giving me the most space I could get out of a box. I just had to take out the shelves and figure out where i was going to drill a hole without hitting the equipment. If you nick a Freon line, it's all over.

Luckily the unit has a small hump on the bottom where it houses the compressor and capillary (the copper tube with very small copper tubes) So I used a 1 1/4 hole saw attached to my drill to just go through the plastic of the interior. It's pretty thin, right under it is the insulation. Using my screwdriver I carefully pulled out the insulation to make sure there was no wires. Once all the insulation was removed from my hole and all was left was the 'metal' housing for the equipment in the back. I just carefully finished the hole without hitting the capillary right under my hole.

here is the location of the hole : https://imgur.com/PmlTTKk

Here's the hole from looking in : https://imgur.com/xfpqz4O

At that point I cleaned it all up and ran all my wires through the hole and used removable tape hooks from 3M for where I was going to run my lines for the Temp controller sensor, the Humidity controller sensor, the PC fan and the Dehumidifier. You can set them all up before you turn on the refrigerator and they'll stick. Once your done and set, you can either stuff the hole with a rag, pillow fiber, or permanently shut it with a can of insulating foam.

I measured the distance between the gap of where the shelves went for rods to hang my product. Using a 3/8 wooden dowel, I cut one in size for reference to make sure it fits, then another trip to the hardware store to get aluminum rods of roughly the same thickness. I then cut them to length with a hacksaw and viola you have sturdy hanging rods. Aluminum isn't cheap as wood, or steel, but it wont break or rust. Onto the equipment..

Here's the equipment I used, there are better products and worse products out there. Your mileage may vary.

Humidity controller: https://www.amazon.com/Humidity-Controller-Inkbird-Humidistat-Pre-wired/dp/B01J1E5LWM/ref=sr_1_5?crid=3NWJ0NHZT7Y9&keywords=inkbird+humidity+controller&qid=1551564548&s=industrial&sprefix=inkbird+humi%2Cindustrial%2C193&sr=1-5

Temperature Controller: https://www.amazon.com/Century-BNQ-T7B-Digital-Cooling-Controller/dp/B01LZV591B/ref=sr_1_3?crid=3A6JON8AZ92KB&keywords=century+temperature+controller&qid=1551564632&s=industrial&sprefix=century+temp%2Cindustrial%2C194&sr=1-3-catcorr

PC Fan: https://www.amazon.com/gp/product/B009OWVUJ0/ref=ppx_yo_dt_b_asin_title_o01_s00?ie=UTF8&psc=1

Dehumidifier : https://www.amazon.com/gp/product/B000H0ZDD2/ref=ppx_yo_dt_b_asin_title_o04_s01?ie=UTF8&psc=1

The Dehumidifier was suggested by another person that uses it as it is rated to work in cold temps (some are not) and it has a small footprint to not take up space.

The PC fan which hangs near the top in the back, I used zip ties to hang it on a set of hooks. I "think" you can see it in one of the pictures. Regardless , just attach a cheap dimmer switch to this so you can set the fan on the lowest setting, you just want a gentle breeze and I only run mine for a few hours a day.

I'll probably get a better Temperature controller. Something that lets me set a range of temps to turn on the refrigerator on and off. This unit turns on the refrigerator when it reaches 2 degrees above my set temp. eh, i got what I paid for.

So, I've set the humidity controller to turn on the dehumidifier when it gets above 75% humidity and the Refrigerator turns on when it's above 55. When the refrigerators temp starts to go down, the humidity drops, shutting off the dehumidifier.

Now when you first place new meat to hang, at the beginning it's going to give off a lot of moisture. So expect your unit to cycle every 10 minutes. Most of the units only run for a few minutes before shutting on, so it's not like they're not designed to go on and off. Hell my apartments refrigerator has been turning on and off for 15 years now, more so in the hotter months.

Oh one more thing, the moisture catch in the back on the unit that sits on top of the compressor. it's designed to catch the water that naturally drains from the unit. Well since we've gone and created a humidity nightmare by adding in 12 pounds of drying meat, expect this tray to fill up. My unit is on carpet in my dining room, so I use a rag to drain out the excess every few days.

I wouldn't want it to overflow and cause damage to my apartment.

That's the cabinet in a nutshell.

This is the one I have. Simple on/off switch so it works with the controller.

https://www.amazon.com/dp/B000H0ZDD2?psc=1&ref=ppx_yo2ov_dt_b_product_details

Hard to give advice without knowing more details (e.g., size of fridge).

Normally I'd say don't bother fixing your rig, just go to craiglist and get a used fridge or upright freezer, but I don't know if you can do that.

Problem with a non frost-free fridge is condensation, which will make humidity hard to control.

Some people gauge humidity with a pan of salted water. A better way would be a saturated solution like these.

I use this dehumidifier, not 100% happy but it works for me. The ones I'd like to use are more for room-sized curing chambers.

You can also use it for ageing cheese, that requires high humidity :)