Unless it is a public safety model Explorer, you probably will not find any suitable wiring.
The radio needs to be connected to the battery to get clean power. Tying into existing wiring is often a source of noise and issues that will drive you nuts.
On the firewall grommet, look for a nipple sticking out into the engine compartment. If this vehicle is like any of the Ford full size pickups, modern GM pickups, etc. you should be able to cut the end off that from the engine side and access that way. I have done installs on a couple of F-350's and was able to get a 6 gauge wire through there.
You'll need to feed a wire through from the engine side, and look for it to come out under the dash. Use that to pull the POSITIVE wire for the radio back through the firewall. Carefully route the positive wire to the battery, cover it in split loom. Install a fuse or circuit breaker (radio should be fused at 15 amps) as close to the battery as you can. Run a wire from the fuse or circuit breaker to the positive battery connection point. Make sure all connections are done properly, use quality crimp connectors and crimp tools. A touch of solder on the very end can help prevent issues. I follow that up with a layer of marine grade/adhesive lined heat shrink to protect the connection and provide strain relief.
Do NOT connect the negative lead to the battery. These vehicles have a sensor on the existing negative lead going to the body that senses current consumption. Bypassing that by running the negative lead for the radio, which in turn will be grounded at the radio chassis and antenna, will bypass this feature. There's usually mention of this in the owners manual.
Instead, run the negative lead to a grounding point under the dash. This provides a short ground path. I usually ground the radio chassis too.
You can use the yellow wire coming out of the back of the radio for ignition sense. You'll have to sniff around the wiring to find an ignition switched source. The ignition switch wire kit from Kenwood (KCT-46) will come with a 3 amp fuse. You can make your own cheaper with a female bullet connector, a fuse holder, 3 amp fuse and some wire. Program the radio to use the ignition switch circuit (with the timer if you want) to have the radio turn on/off with ignition.