Welcome to CA - there a quite a few ex military on here also btw.
Getting to grips with game files etc will take time at first but the right way is to dig in and try things out definately
If the drop tanks appear in the menu only - first open up the F-4ARN_Data.ini (or whatever) and check the correct weapons pylons show the correct model name:
[CenterlineStation]
SystemType=WEAPON_STATION
StationID=5
StationGroupID=6
StationType=EXTERNAL
AttachmentPosition=0.0,0.37,-1.01
AttachmentAngles=0.0,-2.0,0.0
LoadLimit=2050
AllowedWeaponClass=BOMB,LGB,NUC,GP,LP,IFP,DLP,FT,MER,RCN
AttachmentType=USAF,NATO
ModelNodeName=pylon_centerline
PylonMass=31.75
PylonDragArea=0.02
LaunchRailNodeName=
MinExtentPosition=
MaxExtentPosition=
FuelTankName=Tank600_F4 <----model name
To check the model name go to \objects\weapons and open up Weapondata.ini in Notepad (or you can use the Weapons editor)
Do CTRL+F to get a find box - then type in the name IE "Tank600_F4"
You are looking for a TypeName entry like TypeName=Tank300_A6
- see if its there.
If you find it the actual model files for the tank may be missing - check the folder you downloaded and check the tank install instructions again.
If you dont find it then its possible the tanks you installed with the new F-4 have different names - so you will need to find them.