I wired up my cargo light switch to turn on my reverse lights when turned all the way to the right. I have the 2015 style aftermarket mirrors which have the reverse lights built in. I did this so I'm able to see at night when I'm hooking up a trailer or something. The issue with this is that when the truck is started they wont turn on when it is out of park. What do I have to do to bypass this so my cargo lights and reverse lights turn on while it is out of park, I'll use them in drive mostly other than park.

Careful, I'm thinking your reverse lights are controlled via a module. You don't want to back feed voltage into that module.

I'd wire in a second set of bulbs to do this just to avoid what Mike is talking about.

A second set of bulbs would do it.

What do you mean by this? Add in some led cube lights or cut the original reverse lights wires and tap in there?

If you tap into the original wires, you'll be doing what Mike and I warned against.

It'* easy to think of wires like sewer pipes: If I have a sewer pipe (the original wires) and I tap another sewer pipe (add-on wires for your purpose) into it on the downhill end, the sewage (electricity) from either pipe (wire) will flow downhill and light up the light.

Really it is safer to think of them as pressurized water pipes: If I have a pressurized water pipe (the original wires) and I tap another pressurized water pipe (add-on wires for your purpose) into it on the downhill end, the pressurized water (electricity) from either pipe (wire) will flow towards anywhere it can in any pipe it finds its way to, including the light, and also including the module that controls the light . . . which isn't expecting water (electricity) from that direction and might get fried when the unexpected electricity gets there.

That'* why I recommended adding separate bulbs to avoid any potential for this happening. Police/fire/ambulance/roads/tow/etc. do it all the time. Sometimes they use purpose-built kits or have known configurations they can do with lighting systems (like the re-use of reverse bulbs in a Crown Vic for flashing and reverse). Sometimes this isn't possible or desirable (like the flashing blue and red in the reverse lenses that have had strobes added to the lenses while keeping the original reverse bulbs intact).

The Neutral Safety Switch in many older vehicles is a switch that is connected to the gearshift control system of older vehicles. The switch made it so a driver couldn't engage the starter while the transmission had a moving gear selected such as Drive or Reverse etc. With the neutral safety switch you can only engage the starter while the transmission has Park or Neutral selected. Because of this, inattentive drivers were no longer accidentally starting their car only to have it start mowing down small children or a planter full of azaleas or their boss as soon as hydraulic pressure built up in their automatic transmissions.

A side benefit of the Neutral Safety Switch is: Now there'* a switch there with electricity and everything, and it knows what gear range has been selected. It isn't much to add a circuit to the Neutral Safety Switch that would light up a couple of bulbs on the back of the car. So that'* how it was done by pretty much everybody for decades.

I'm pretty sure the 2013 Silverado in your profile controls the lights with a module instead of a mechanical switch. It is part of "nowadays" where the transmission gear range selection is signaled to a computer, and the computer decides what to do with it. In your case, you select Reverse, the computer tells the transmission whatever it needs to, corrects idle speed for the extra load, starts watching the wheel speed sensors for movement, continues lighting up the brake lights that you were pressing while shifting because you are a safe driver, and lights up the reverse lights. No Neutral Safety Switch involved.