how to power led strip

That link doesn't work either (notice the # after http://?) - but all that is ever needed for eBay is the magic item number (250587661043). Yes sir - we have the technology....! First comment - I hate sites that do not include IMHO is basic data - like connections else individual LED data. However, at least they state "High brightness 3528 60 SMD warm white LEDs" and 3258 leads me to $0.18c 3258 (1205 sized) White hi-intensity SMD LEDS with Forward current: 60mAh (sic!) & voltage: 2.9 to 3.3V. So they are 3-ish volts. So again.... 60 LEDS (ie parallel strings) @ 2A = 2A/60 33mA per LED, hence they are wired 2 in series, so 30 strings @ 60mA = 1.8A (ie, their 2A). 2 max-3.3V LEDs means 6.6V, so the resistor is dropping about half the supply voltage. Half of the energy consumed is being wasted in resistors as heat. But being SMD etc, and being 30 parallel strings, I doubt that you'd want to rearrange the strings (eg to 4 in series for a total of 15 strings and hence 0.9A consumption).    It's back to the 2AH per hour of operation. 6AH per 3-hours day (or 6AHx12V - 72 Watts per day which might get by with a 35-40W solar panel with reasonable 12-hour sunshine....). Or one 12V-7AH battery per day (~$35 for an AGM). Or ~40AH for 1 week ($140) Or 160AH for a month... hmmm (Odyssey 65-PC1750 is only 74AH ~$280), or 31-PC2150 or 31M-PC2150 (90AH) ~$350 or PC2250 (100AH) ~$450. But be aware that those AH ratings are over a 20-hours discharge period aka the C-20 rate. You really want a C-90 rate for a month at 3 hours per day (sort of), and AH capacities increase with longer discharge times (ie, lower discharge currents). EG - those C-20 100AH rating become 92AH at the C-10 10-hour rate. You get an idea for what your are up for.... Unless I have boob'd again in my calcs and approach (any sanity checkers out there?). You may find that halving the current per LED (ie, to 30mA) makes little difference for what you want, etc. So if you removed all resistors and replaced them with the "remaining" 2 LEDs from other resistor-less strings (hence from 30x60mA to 15x60mA strings = 1Amp (900mA)... And ran at half current (is 3/4 or half or 1/4 brightness?)... That's 450mA - 1/4 the original current draw (40AH per month). Otherwise just replacing the resistors with 2 LEDs halves the current draw.