That's extremely interesting. The frequency band is well within what you could do with fairly simple gear. Assuming it is still alive just reaching it would already be quite something, getting some useful readings from it would be absolutely awesome.
This may be something where talking to the HAM community will be more productive than talking to the hacker community, the first step would be to reliably track it using an antenna suitable for the frequency range and checking if it is emitting anything at all before attempts to contact it would make much sense (once you have a signal to home in on it is a lot easier to prod it rather than to prod blindly until something responds).
Keep in mind that this frequency band is not exactly unlicensed territory, you're smack in the mobile aeronautical band according to ofcom. So listening is likely ok but you may need a permit to transmit at that frequency and it is not necessarily the same frequency at which the satellite will receive it's input (typically it is some other frequency to enable full-duplex).
The amateur and academic radio astronomy community may have suitable antennas. Do HAM radio operators use dishes? I thought they use mainly vertical/dipole setups?
Sure they do. In fact, the microwave band was used for the longest time by HAMs because there was no known application for it, they pretty much pioneered it and dishes were the antennas of choice for those frequencies.
Doing a 1/4 wave trackable parabolic dish for something a little under 3m wavelength is very much achievable (and is not even close to microwave frequencies, 3m is huge!). If you want better efficiency you could use a larger dish but I think that it would be easier to up the power on the transmitter than it would be to make a dish 4 times that surface that rigidly tracks an object in LEO. That's quite the little bit of hardware engineering you'd have to do there. Even a few degrees 'off' would likely ruin the signal so precision is key and a large dish catches a lot of wind.
This may be something where talking to the HAM community will be more productive than talking to the hacker community, the first step would be to reliably track it using an antenna suitable for the frequency range and checking if it is emitting anything at all before attempts to contact it would make much sense (once you have a signal to home in on it is a lot easier to prod it rather than to prod blindly until something responds).
Keep in mind that this frequency band is not exactly unlicensed territory, you're smack in the mobile aeronautical band according to ofcom. So listening is likely ok but you may need a permit to transmit at that frequency and it is not necessarily the same frequency at which the satellite will receive it's input (typically it is some other frequency to enable full-duplex).