new alternator new battery new plug no charge

[calisvx]

sorry typed on phone

Hi guys iam restoring a pearlie from the junker and have it almost done but iam stumped on the charging system i changed out the battery and purchased an alternator from napa a 110alt gold series i believe, and fixed the plug that was giving me christmas lights. all this time and the @#$ plug was the culprit oh well its fixed the car starts no christmas lights no warning lights car just runs until battery dies alt does not kick in all the wires have been fixed checked continuity and everything looks good what gives????
I purchased a tester from harborfreight what do i test to find the problem?

battery fully charged sits at 13 car on 12.5 then after like 10 min 11v and just drops to below 10 withers and dies i had both batt and alt checked they passed all tests under load and bench what do i do guys