Thank you Benjo for explaining. Let me give you something that would be plausible.
- If the child is fully deaf, full stop -
If not...
Now, I'm figuring the child is not totally deaf, as they are using the Phonic Ear in school.
The child could have a 49MHz VOX headset radio back in the 1980's. He could crank the volume to full or someone could have wired an earphone for it, due to his needs. I believe those things were $50 for a pair, so someone else has the other like another kid he would talk with. Those radios had VOX (voice activated transmission ability) so no need to press a button.
That VOX will help in two ways:
1. It only transmits when the audio level is loud enough to activate it.
2. Since it is not always transmitting it will save on battery life. (Those things used 9v batteries)
There are several things you are going to need to stretch here on the plausibility:
1. How long the battery lasts. If the child is able to turn it on just before leaving the van, that would be good but not mandatory. Still, having it on for several days would be a stretch, even if only occasionally transmitting.
2. I presume that radio would be in a bag, so figure out a way to get the bag near the window of the van. Alternatively, can your antagonist live in a two story building? Have them take the bag with other stuff from the van and put it near a window. If it needs to stay in the van then leave it, but if it could be on the dash or near a window it would help.
At this point we have a device that was around back in the 80's and occasionally transmitting on 49 MHz.
3. Your protagonist may need to be a radio buff, or their uncle is or someone. This is where the frequency hunting gear will come in. Back in the 70's there were portable radios $50 that could receive AM and FM broadcast bands as well as amateur radio, and bands used by police, fire, etc. Have your protagonist turn on the other VOX headset radio and then use that wide band portable to dial in on the exact frequency. That is critical.
They could then use this wide band radio, which is portable, and do the body fade once they heard a signal. Have them go to the top of a building or hill in order to get an initial bearing. Also have them bring along the other VOX headset. (They could attempt to use the VOX headset only, but the antennas on those things sucked. You could probably get away with using only that, but that would be a stretch and you don't have to do that because of the wide band radio.)
If your villain is in another town, this whole premise will not work. Those little radios do not transmit that far. If your protagonist is an amateur radio buff, which would make sense as why the child has the headset in the first place, you really can make this plausible. Or perhaps the child's uncle if the protagonist and child are unrelated. The amateur radio buff will be able to put together a dipole using Hamsticks in the 6 meter band. The six meter frequency ranges from 50 - 54 MHz, that makes it an antenna that is close to 49MHz and provides improved receive and directivity, to some degree. The coaxial cable going from the dipole antenna would plug into the wide band radio. An adapter would be needed but you can gloss over that.
A dipole antenna has nulls. If your protagonist is standing holding a pole that the two 6m Hamsticks are attached to (it would look like the letter T) and he is looking north, the nulls will be toward the east and west directions where the arms of the antennas are stretching out in both directions. A null is the direction or directions where the antenna does not receive signals that well. Again, if he is looking north, he would hear better in that direction and equally south, depending on what terrain is in the way. (Or you could simply write that they turned the antenna to find the direction. hahahaha that would be much easier than killing the reader with too many details) ahaha my long explanation is to make it plausible in my head.
Anyways, you pretty much have it. The protagonist may need to drive and wait and drive and wait until the villain makes noise, or turns on music or a TV that triggers the VOX. Once they get close, the protagonist could use the other VOX headset and listen to the villain as he approaches the location. Perhaps the villain is snoring or something or still listening to music.