The Auto on my Boss RC2 sometimes doesn't seem to pick up a signal and engage. It is plugged into a multi- socket adapter and I do not have the amp turned up too loud as the room is tiny. I thought it was supposed to pick up a signal no matter how strong. Maybe if there's any interference from any other close by source this could be the cause?

Can you get a cable adapter from somewhere like ShowMeCables similar to this:
https://www.showmecables.com/by-category/adapters/audio-video-adapters/3-5-mm/3-5mm-stereo-male-to-dual-1-4-in-mono-female-adapter-cable-6-in
Use the headphone out and plug your amp into the left channel of the adapter.

Yes. There should be a mono out on the unit and that's what ypu'd use.

http://www.ebay.com/itm/DC-9V-AC-Adapter-Casio-CTK-4000-CTK-558-CTK700-Keyboard-/221021599357

Boss ME-25, use polarity like boss stompbox.
+ voltage at the ring, and - voltage at the center pin, of the adapter
connector.
..
At ME-25 DC socket:

Depending on the model, there are four around that date, it could be the insert jacks are tarnished reducing the signal flow between the pre amp stage and digital power amplifier. It could be the power amplifier has failed. It could even be customer error in wiring.
This assumes there is the correct level of signal entering the input sockets of course.

Verify that you are using the ORIGINAL power adapter... NO substitutes are allowed.

The half-way cord is the clue. Read up on unbalanced and balanced lines and TRS connectors.
One of these requires TRS connections and the signal is being carried on the RING of the TIP-RING-SLEEVE connector. Plugging in half-way the TIP touches the ring pickup contact. The emgs one MAY use TRS type cables and there may be a reason the signal and hot of these are reversed. If I could find schematics on all this equipment I could unravel the exact cause. You could make an adapter with a Stereo 1/4 inch plug and a 1/4 inch jack by wiring it to swap the tip and ring between them to use for connecting to the emgs guitar. ALSO verify you are using the SAME type guitar cable for both.OFTEN a TRS cable will NOT turn on the electronics when plugged into a guitar. Use an unbalanced instrument cable unless you have the XLR type output. Use of an adapter from the XLR type cable into the Boss will usually not work.

A few things to try....

Usually the adapter will over ride the battery when used.
1) Make sure your 1/4" cables are working properly without the pedal "in-line".

2) Take out battery, and use just the adapter only. Make sure it is the correct and proper adapter that works with Boss. Usually the PSA-120. If you are not using a Boss Adapter, make sure yours is a direct replacement with same specifications. 9V/200mA. And "tip negative". DO NOT use Radio Shack stuff, nothing against them, but there adapters just don't mix well with Boss products and the like.

2) Try just the battery, no AC adapter. Remember to unplug the input when not in use. Saves battery.

Basic rule of thumb...when using correct AC adapters for all your pedals all the time, and all sounds good, then take out the batteries.

If you still experience problems, it would be an internal IC chip most likely. From there post another question maybe.

sounds like the true bypass line has been damagd. Should be easy enough to fix. Pop open the unit and do a visual inspection first, if nothing is noticeable then do a continuity check with an ohm meter from input to output with the delay efffect off. If you don't read a short in this situation then your problem lays within the signal path and its switched path.

You will have to test the adapter with a volt ohm meter to make sure it is putting out the proper voltage. It should be as close to 9 volts as possible. Also make sure that thehole in the plug is negative and the outside is positive. Is it the right adapter? I don't have a schematic for this model but www.schematicheaven.com has one for a DD-2. Hopefully they haven't changed too much. If you decide to repair it yourself, check the adapter first then check for a bad solder joint where the adapter plug is soldered to the circuit board. Hope this helps somewhat.