I have uninstalled all FSX and reinstalled only FSX, TacPack with F/A-18 and J35J. I have no other add-ons. This is to test TacPack on J35J without any extra disturbances.
And my suspicions were correct – now I can use the drop tanks for J35J without problems.
Windows 10-64, FSX Acc, Acer Aspire xc600 3.00 GHz, 12 GB RAM, AMD Radeon HD 7000, Saitek FLY5 joystick, TacPack v 1.4.2.6