Printer still printing extra page after each printer page/New driver did not work

OK, lets be sure that it is the driver problem only, and not a combination of the printing program and the printer.
Is it the same problem if you print from pdf?

The laser jet 1320 is a very old printer (about 10 years old now) and therefore driver support is very limited.  Problems like this are very common.  You have two choice with the driver.

Download the universal driver from HP and try and see if that works. https://support.hp.com/us-en/drivers/selfservice/hp-laserjet-1320-printer-series/410622/model/410627 Chances are it won't

Download the drivers from microsoft catalog http://www.catalog.update.microsoft.com/Search.aspx?q=%20HP%201320%20windows%207 Better odds here Try the PCL 5 drivers

If no changes printing from other programs.

Then it's time to look at the driver.

For basic printing functionality use the Postscript PPD or one of the PCL drivers.
For advanced functionality such as printer status and maintenance features, use the HPLIP driver (which includes HPIJS).
For this troubleshooting use the Postscript PPD or one of the PCL drivers.

Does it make any difference selecting different versions of the driver?

I would try this document (or some documents) on a different computer with a newer printer.

You could have a hardware problem in the printer or (as noted above) it could just be the age of the printer.

With Word I get an extra page and no duplexing; with pdf just no no duplexing. Checked MS catalog and the only PCL5 drivers are old driver UPDATES. The other 1320 drivers are either DOT of DOT4 - not sure what that means. Tom not sure where to get the postscript driver. Driver that is installed is labeled "hp laserjet 1320 series UPD PCL 5." That was the only driver for a 1320 on HP site. Not sure how to "switch" between drivers unless I install two. The universal print driver link takes me to a 1320n. I can certainly try that. Finally, there is no listing of the drivers in "programs or features." I have to use the print management utility.

So what you have discovered is that the installed driver performs differently depending on the program who prints.
The printer driver acts like a translator to the printer, and you will need one driver for each language needed (PLC6,PLC5,PS and so on)
When you are using a newer version of a program (Word) and a outdated driver (translator) you run into compatibility issues.

With no support (updated driver) on the  printer, you are in the find and try land.
You might find a universal driver who will work 100%, or you will end up in a compromise situation (putting the blank paper back in the bin) :-)

For now, install all the driver types you find for your printer. And try them out one by one.
Warning: only download from official sites! not those "we have a driver for you, click on the exe file"

"The universal print driver link takes me to a 1320n"
Start with this driver.
n means network printer, but it also have support for USB

What is the result if you print to a PDF/xps the same document?
what happens when you print the rest age from the printer that display the printer settings?
See whether you can coke reset the printer (power up while depressing the enter/go button on the printer)
Either that the properties somewhere there it triggers the output of a blank .......

Als check that Duplex is installed in the driver

Control Panel - Hardware and sound - Devices and Printers -
Double Click on the Hp Laserjet 1320 series UPD PCL 5 -
select customize your printer - Device settings tab
Look for Duplex unit - make sure it says installed

It is not driver problem. You need a cleanup of the interior of your printer. Details as follows:

1. I have cleaned the cartrige are using a soft cloth. there is especially a sensor at the top of this area; try to clean it gently. Also play with cartridge itself gears and its paper sensor (at the left side)
 
2. make printer to go trough a self-cleaning process; this is the process:
on the printer control panel, press and hold the Go button until all threee lights illuminate (about 10 seconds). When ee lights illuminate, relase the Go button.
 
for best result use a sheet of transparencyl If you do not have any transparencies, you can use copier grade paper (70 to 90 g/m) that has a smooth surface.
Be carefull don't use plastic transparency. Transpaerncy papers are different that transparent plastic sheets that usually are used for binding purposes.

Source: https://h30434.www3.hp.com/t5/LaserJet-Printing/HP-LaserJet-1320-Print-extra-Blank-Page/td-p/5334814/page/2

If cleaning does not work, it is a hardware problem of paper sensor. You need to have the printer serviced.

Press the green button on the printer, it will print a test page.  If the test page prints correctly, then you know it's a driver problem for sure.

Have run all tests suggested. Same results. All 1320 drivers have same version number as one installed. It's a UPD. Checked and toggled on and off all duplex settings. Getting all kinds of results - no duplexing, duplexing with one side of page blank. Sorry but the cleaning did nothing. If it's the hardware, not point in servicing. Might as well replace machine. Before I close the question, any more suggestions?

A test print using the green button on the printer will give a blank page also?

can you test the printer on anothe r PC ? that would tell you where the problem lies - with the printer, or PC

Going to get HP LaserJet Pro M203dw Printer. Thank you John for steering me to print management. Only way to remove the old drivers. Thanks to everyone for the troubleshooting tips.

You are very welcome and I am always happy to help you