I've had problems with the tip connector on Switchcraft jack sockets in both the up and down positions. It definitely won't go sideways, so you need to pick up or down. Sometimes 'up' will move the end of the tip connection against the end of the rout, so that you can't insert a jack properly. And sometimes down' will touch the floor of the cavity. A lot depends on the routing of the cavity, and the positioning of the screw holes for the plate. Pure Tone jack sockets make it so much easier with their much shorter tip contacts.
I feel that twisting wires will give some improvement to noise pickup, but not much. The idea of the twist on a balanced differential input arrangement is that both wires pick up equal amounts of noise - especially so when close to the source of noise when the noise wavefront is still spherical and the noise amplitude can vary significantly over a short distance. The tighter the twist, the better the noise matching will be, and the better the noise rejection will be.
On an unbalanced input arrangement, any noise reduction can only be by the ground wire being between the signal wire and the noise source and absorbing the noise signal before it hits the signal wire. At best, you've got a theoretical 50% coverage, which would result in a maximum 6dB drop in the level of noise picked up by that section of wire (which may be insignificant in comparison to the noise passed on by a single coil pickup). But if you say that vintage push-back wire has a core that's about the same diameter of the thickness of the cloth covering, then the actual amount of signal wire protected by the ground wire becomes a lot less, and really only where the wires cross. So the level of reduction bay only be 1 or 2dB. All worth having, but it's never going to keep the guitar quiet in a noisy environment. At worst, it won't do any harm, so you might as well do it.
It's the 'differential input' that does most of the noise reduction work with a balanced differential input. The 'balanced' part of that indicated that both the signal wires are at the same (high) resistance to ground, which primarily stops the risk of ground loops that can occur on unbalanced systems where one of the wires is tied to system ground. Any ground loop on a balanced system can be removed by breaking the shield connection at one end.
But balanced also allows one signal wire to be sent as one positive and one negative signal with respect to each other. Any the noise signal picked up by both wires is the same polarity, instead of opposite. Fed into a differential input (which sums the difference between the two signals), the original signal amplitude is doubled, whilst the noise signal nearly all cancels out.
So you need both a balanced system and a differential input for a twisted pair to work properly.
The EMI noise rejection/reduction is normally between 70-90dB with a balanced differential system and a tight twisted cable, which is why simply twisting the wires together for somewhere between 1-6dB of noise reduction is never going to compete. Using screened cable is far more effective than just twisting the wires together..
Twisting wires together certainly significantly reduces any outgoing noise. As the current flowing in each wire is equal and opposite, so will the magnetic/electrical field they generate be equal and opposite. Twisting the wires gets them as close as possible, so that most of the two fields generated cancel out, with minimal residual noise emanating from the pair. It's why heater wires in valve amps are twisted together. It may be a low voltage - typically 6.3v a.c. but it's a high current, and it's current that generates the noise fields. Without doing this, a lot of 50/60hz hum can be transmitted to the amp circuitry.
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