There is a distinct possibility that the alternator has a faulty rectifier which is allowing too much AC ripple in the output. Alternators generate AC current (that is why they are called alternators); this is changed into DC by means of some heavy duty diodes utilized as a rectifier bridge assembly. If the rectifier has a faulty diode, it will allow some AC current to leak through into the output.
Most vehicle electronics are highly sensitive to AC current, and will often act strangely or not operate at all if the power supplied to them is not pure clean DC.
The quickest, easiest way to check for this is to use a lab scope to check the alternator output for excessive AC ripple. Many carbon pile charging system analyzers also have built in a ripple test, although this is not as accurate as scoping the output. Just because an alternator is new does not mean it cannot be defective, particularly if it is a cheap discount store alternator.
I would recommend taking the car in to a technician equipped to scope the alternator and check the waveform for AC; this is a very easy, quick test that usually does not cost very much.
By teh way, connecting/ disconnecting the alternator output while the engine is running or teh key is turned to the ON position is not a recommended practice; this can easily generate voltage spikes capable of damaging electronic components in the vehicle. Also, operating an alternator with no load connected to the output will quickly cause it to overheat and cause internal damage.
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