Is the headlight control module part of the body control module, or is it a separate part?

According to this there isn't one

https://fuse-box.info/dodge/dodge-caravan-2001-2007-fuses

And this confirms there isn't one. The are controlled by the Body Control Module.

https://www.chryslerminivan.net/threads/both-headlights-went-out-on-my-dodge-caravan-2005.82722/

No headlight relays or fuses on your model year. It is all controlled by microprocessors in the Body Control Module (BCM) and Front Control Module (FCM). You can try resetting them by removing the IOD memory fuse in the fuse box or the negative battery cable for 5 minutes. Have you tried cycling the headlight switch many times? Still out? There is an extended lifetime warranty on 2005/6 Dodge/Chrysler minivan headlight switches:
http://www.aboutautomobile.com/Investigation/2005/Dodge/Caravan/Headlight+Switch

It also mentions above there was a recall on the headlight switch

https://www.google.com/search?safe=off&rlz=1C1QJDB_enCA643CA644&sxsrf=ALeKk03EyFMxR9dby9JKQqr3KZhyDQ3SrA%3A1612641772078&ei=7PUeYPahBIWk_QbM57ngBw&q=2004+dodge+caravan+headlight+fuse+location

..

Did you check the high/ low beam headlamp relay ? Stuck contacts in side relay .Plus headlamp relay an DRL relay .All are located in the underhood relay center .
The headlamps are controlled by the body control module (PZM). The battery positive voltage (B+) is applied at all times through the HDLPS fuse at the switch side of the headlamp relay via CKT 340 (ORN).
Battery positive voltage (B+) is also applied at all times through the RADIO/PHONE fuse to the coil side of the high/low beam headlight relay via CKT 40 (ORN/BLK). Both relays are controlled by the PZM at separate output cavities.

When the headlamp switch is in the HEAD position, the instrument cluster headlamp switch input is grounded through CKT 10 (YEL) and the headlamp switch. The instrument cluster sends a request through the Class 2 serial data line to the BCM in order to active the low beam headlamps. The BCM supplies positive battery voltage (B +) to the coil side of the headlamp relay via CKT 352 (WHT). The coil receives ground through the headlamp switch via CKT 10 (YEL). The coil of the headlamp relay is then energized, closing the switch contacts. Battery positive voltage (B +) is then applied through the high/low beam headlamp relay via CKT 1346 (LT BLU) and the L HDLP LO fuse and R HDLP LO fuse via CKT 12 (TAN) to the left and the right low beam headlamps respectively.
This may sound pretty complex .
1
Was the Headlights System Check performed?
--
YES - Go to Step 2
NO - Go to Headlight System Check
2
Are the park lamps also on?
--
YES - Go to Step 3
NO - Go to Step 13
3
Connect a Scan Tool to the data link connector (DLC).
Inspect the IPC headlamp switch input.
Does the headlamp switch operate properly?
--
YES - Go to Step 4
NO - Go to Step 10
4
Disconnect the instrument cluster (IPC) connector C3.
Do the headlamps and park lamps turn off?
--
YES - Go to Step 5
NO - Go to Step 6
5
Replace the instrument cluster (IPC). Refer to Instrument Cluster Replacement in Instrument Panel, Gauges and Console.
Is the repair complete?
--
Go to Headlight System Check
Is the repair complete?

6
Disconnect the body control module (PZM) connector C2.
Do the headlamps and park lamps turn off?
--
Go to Step 7
Go to Step 8
7
Replace the body control module (PZM). Refer to Body Control Module Replacement in Body Control System.
Is the repair complete?
--
Go to Headlight System Check
--

Your best bet is to take it to the dealer .

Year/make model???? Possible daytime running light module shorted out

Headlamp control module ????? No such thing on your vehicle !
Has a DRL - daytime running lamps control module . If you were to put headlamps in the on position an they don't work ,this module has nothing to do with them not working .Google what the part looks like .It's location is below left hand side of the steering coulmn . Has two connectors of wires , a bigger box is below it with three connectors of wires . this one is the BCM - body control module

This vehicle has what is called a TIPM (totally integrated power module). It is actually the whole underhood fusebox/relay center. It is a module and is where the headlamps recieve the power when the pcm and body control modules recieve signal from the headlamp switch. Very common for these TIPM units to go bad causing this type of problem. TIPM usually costs around $650 new from Chrysler. May be able to find a used one. No programming is needed when replacing this TIPM. I would suggest having it at least diagnosed by a qualified technician before investing in the replacement. Hope this helps.

I had a similar issue that was repaired at the dealership. They replaced a relay switch to fix the problem.

I found one for $408 at www.mazdapartscenter.com.

sounds like possible headlight switch, but my guess is a bad bcm '' body control module'' youll save money in the long run if you took it to the dealer for a diag, they the know the product,

anything related to headlamps, instrument lights, door locks, etc... is typically related to a separate module called the BODY CONTROL MODULE (BCM)

Not sure about a body control module, there is a pcm under the hood on the pass. side that controls most everything on these, however i would check your fuses for the seat, on the 00 models the headlights do stay on all the time while driving due to daytime running lights but if they stay on after you take the key out then id check the headlight switch or sensor on the pass side dash.