I have several Hall Effect sensors saved from a VCR. I'm guessing they are thin film Indium Arsenide type. Using a standard analog multimeter, resistance Rx10 scale, to measure resistance across any two of the four terminals, I notice an increase in resistance when a magnet is placed next to the device. In this case, resistance changes from about 330 ohms with no magnet present to about 400 ohms with the magnet directly next to the device case. There seems to be an area of proportional change as the magnet approaches.
Of course, I'm aware this is not the usual configuration for Hall devices.
What do we know of this behaviour?

Do you understand how the Hall effect works?

I'm not sure exactly what you want to know.

This effect, where the longitudinal resistivity depends on field strength, is sometimes called the "longitudinal Hall effect" or more commonly just magnetoresistance. In most materials this effect is rather small. For Hall probes, the most significant effect is usually to change the Hall coeffecient by 5-25% per kG (lower for InAs and higher for GaAs). However, in some materials, especially magnetic thin films, the phenomenon of giant magnetoresistance is possible where the above effect is rather pronounced. Now, I'm pretty sure thin film InP is a component of several systems displaying GMR, but I don't know about thin film InAs. If I get the chance, I'll look into it for you, in the mean time, I might could say more if you could provide some more data.

Although I don't know for certain, I would suspect that the Hall sensors from a vcr are hybrid devices. They probably incorporate an ic chip, and have whatever response curve the designers wanted. Just the swag of an old etech. ;)

Physics Monkey, your explanation is good, I believe you've provided a few keywords which also may prove helpful. I've been mostly searching online for this. Thank you. :)

Kevinalm, yes, I'm somewhat familiar with the integrated devices and have some I've been comparing. These seem much simpler. I'm thinking they're from an 80s VCR. The circuit board (part of the head assembly) appears to have the necessary other circuitry. Thank you. :)

Even back in the 80's, they would likely have some internal active component(s). A transistor for example. But it is possible that they are "naked" hall sensors. Your best bet would be to try find the manufacturer's spec on the part. Good luck, your probably going to need it. ;)

Bear in mind also that they were in all likelyhood intended to be used in a digital mode. An on/off or go/nogo situation, so there is no guarantee that they are suitable for variable position sensor for example. But hey, you got em, play with them. Sometimes that's the best way.