Since this is rental property, you're probably not going to want to do the permanent-type improvements (ground conduits, etc) you might do otherwise. Here's a quick way that I would try: Get a planter or pot that's about the width of that pole-to-fence area, and plant it as you will. Run your cord through the center, with the join, or timer, or whatever electrical connection you use in a BOX nestled in the planter.

We've found from experience that trying to enclose the plug in a plastic bag is a disaster -- water always gets in, and can't get out... so we use a wood or metal box, with drainage holes in the bottom. Then attach your rope lights (don't you love them? -- we have them under our deck, so the dogs can see to "go" on rainy nights0

first time that I have been here, and certainly pleased that I stopped by. I also have been lightening up my front area with rope lights and "shop lights for years. All strung together with electrical cords (outside approved). Every now and then I do have difficulty with water getting in somewhere, during a heavy rain storm, that makes my outlet "pop" off. Haven't found the "cure" for this yet. Have traced all cords and bagged and even unplugged some to see if that was my problem. Don't have problems with snow. This is so pretty at night it is worth the effort and I have an elderly lady next door that waits for my lights to turn on each night. Somehow gives her comfort. I do have mine on a timer. Thanks for letting me share

Alison low voltage lighting is the way to go. Easy to put in, safe, and you can remove it if you move.
The link is for just one set but there are sets for stairs that will go esily on the fence.
Ive seen 20 light sets for under $40 dollars.

Here is a link that might be useful: Low voltage lighting.

I just "installed" a three spotlight string of solar lights, which use one large solar panel that can be placed wherever it would get the most sun. I have one spot bouncing off the base of a double birch clump. one off the corner of my fence and one further down. It was surprisingly bright WHITE light for a solar yard light. The wires are rather long, so the solar collector can be placed some distance from the actual spotlights, which can be placed in full shade and will still work. Mine was by Malibu and was 20% off at Home Depot. They can either be staked in the ground or mounted to wood (two base options). Two sets of these could provide some nice light and require NO wiring.

The low voltage and the solar lights are certainly something to consider. I've got to take a notebook out to Lowes and Home Depot this weekend to compare prices and setups.

There are two things that appealed to me about the rope lighting option. The first is that, tucked under the top stile of the fence, the light would be fairly subtle, more of a glow than a specific light source.

The second is that, depending on how closely I space the brads holding the rope to the fence, it would be pretty hard to steal. As you can see from the picture, the alleyway is pretty exposed.

I'm thinking the solar lights could be really nice on the front porch, as well. The landlord has rewired the light fixture 4-5 times in the 10 years I've lived there, and it always blows out immmediately. I don't like not having a light on the porch. If I suspended the lights from the porch ceiling, I could put the solar panel out on the front of the apartment, which gets 10-12 hours of sun a day.

Might be too much solar power!

Thanks for all the ideas!

Alison-
I too like the rope lights, but, I'm also quite fond of my Malibu lights from the Depot. They're low wattage and cheap. 10 lights and the power pack with timer for around $25. No need to use all of the lights if you don't want that much light, but, can always add the others if your needs change. Very easy to install.

Here is a link that might be useful: Home Depot Malibu lights

Alison, I don't know what your neighbors are like, but I've had solar lights stolen. Whatever you choose, be sure to secure them well. I also think people are less likely to "lift" something that is installed than simply stuck in the ground. Good luck!

We bought a cord cozy. I am thinking I found it in a pond/water garden catalog. Might search through the sites there. Sorry I can't remember where I found it at but they do exist.

im not an electrician but I work for an electrical supply house. Ive seen just about everything under the sun that is made for lighting. The plug outlet on the pole may or may not be hooked up to the photo cell of the lamp head. Simply plug a light into the outlet while the lamp is off to test if the plug operates on the same circuit.If it turns on while the lamp head is off then of course your rope light will never turn off. If the outlet is always energized then I would purchase an inline/plug-in timer and do and hide it under a pot. If the outlet turns on and off with the lamp head then you could purchase a rubber boot made for covering extension cord plugs. You would probably have to order from a supply house. For the pole outlet, a weather proof in-use cover might work, though I'm not sure if it would mount to a round pole.