Monday Monarch LGW-TCP flight operates on 757.
You are not likely to see much down there and the airport is particularly unfriendly for any form of observation due to its location and layout. Tour operator transfer buses between the airport and resort are the only effective means of transport unless you want to try a taxi from your hotel; but there are rarely taxis at the airport for a return journey. There is the odd flight (every two weeks or so) from Czech Republic and an occasional visit by a Russian IL86 or 154, but all of the rest of the traffic is from the UK - TUI, First Choice, Monarch, Astraeus and Excel all operate once or twice a week, mostly on different days to each other. Otherwise, forget it! You also won't see any form of comings or goings from your hotel, which are down the mountain beside the Red Sea - the airfield is on the top of a plateau around 2500ft above sea level, which makes the coach journey interesting
One thing you might like to do; if staying in Taba resorts, it's quite easy to get up to Eilat for a mooch around town by using taxis from your hotel to the border (agree price before you set off; probably 20-25 dollars) and then going on foot through the Egypt/Israeli border controls (no border fees) before picking up an Israeli taxi for the last 2km or so into town (change some currency in the bureau de change inside the Israeli bit of the border post). Shopping and restaurants in Eilat are OK. Eilat airport is right in the middle of town and it is an incredible sight watching 757-300s on approach over the shopping centre into the old town centre airport just across the road. There are a couple bars on the beach very close by. From memory, Thursday is the busiest day (running into the evening) and you should catch the various Arkia, Israir and El Al flights running up and down to Tel Aviv. There aren't any international flights there as they op to Ovda where runway length is longer, but it's still fun to watch.