A beady-eyed sea horse seems to be staring at us. Polite or not, we're certainly staring at him . . . and at a Sea Lily, looking more like a peacock than the fish it is . . . and at a box fish (rectangular, really, but resembling the carton it came in).
They couldn't be easier to see if they were in a home fish tank. But these denizens of the deep aren't in a tank - in effect, we are.
We are in the underwater observatory at Coral World, just seven miles south of Eilat in the Coral Beach Nature Reserve. There are many other aquariums in the world, but only three similar to this one. For at Coral World, the people are enclosed; the fish swim freely in the translucent waters of the Gulf of Eilat.
The Gulf of Eilat is the northernmost extension of the Red Sea. Despite the name, the sea here is not red; it is indigo (it was originally called ''Reed Sea''; one ''e'' just got lost somewhere through the centuries), except for glimpses of other colors in its depths given off by a coral reef and the various species of tropical fish that call these waters home.
There are some 800 species of fish in the Red Sea, compared with 300 or so found in the Mediterranean. That makes this area popular with skin divers and scuba divers.
If you want to take diving lessons or rent equipment, there are any number of places in town to do it: Aqua Sport, Red Sea Divers, Lucky Divers, Neviot Diving Club. But you don't have to don any gear - for that matter, you don't even have to get wet - to see fish here. Just walk the 100-yard-long pier to Coral World's observation room. Once there, descend the spiral staircase to the portholed chamber 20 feet below water level.
It's conceivable that from this vantage, every fish in the Red Sea could glide by. And every one that does will look as if it's been costumed for a Hollywood spectacular: a wrasse, its elongated body painted in the red, green, blue, and yellow wriggles, squiggles, and spots of a Jackson Pollock. A stonefish in green and fuchsia and oatmeal, resembling the colorful coral scree at sea bottom it hides among.
A spotted wrasse wears dotted Swiss. The angelfish is dressed down; it sports a home-knit sweater of orange and purple stripes. A lion-fish is dressed up; it's very formal in layers of lace at 8:30 a.m.
Perhaps it thought it was being reviewed by royalty. After all, its forebears probably were - not once, but many times over. It's in biblical record (I Kings 9:26) that King Solomon ''made a navy of ships at Ezion-Gaber, which is beside Eloth on the shores of the Red Sea.'' He sent his navy south to bring back spices and gold from the land of Ophir.
It was from that same direction that the Queen of Sheba passed through here on her way to visit King Solomon.
Another navy was built in Ezion-Gaber by King Jehoshaphat of Judah in the 9th century BC. And, 2,000 years later, the Crusader king Baldwin I took over the town. In the interim, it was home to the Ptolemies of Egypt, the Roman Tenth Legion, the Byzantines, and, several times, the Arabs.
Today about 21,000 Israelis live here, and Eilat has become a winter playground for the rest of the country's population. For that matter, because of its beachfront location, pleasant weather, and convenient charter flights, winter-weary Europeans and Americans flock here, too.
The average temperature November through April is 80 degrees F. and the air is desert dry. There is good reason for that: Eilat may face the sea, but it backs up against Sinai's sandy and red sandstone wasteland.
In fact, one of the more interesting ways to spend a day here is on a desert trek. Johnny Desert Tours, for instance, will take you to Red Canyon and the Canyon of Inscriptions for about $35 a person. You can visit with a Bedouin and see an area that formed part of an ancient caravan route. The Canyon of Inscriptions still bears ''graffiti'' of travelers from past centuries: Nabatean , Greek, and Hebrew messages adorn its granite walls.
There are other tour companies - Egged, Kopel - and other tours, lasting anywhere from half a day to three days, which give glimpses of monasteries, oases, Bedouin camps, and biblical history: One of Egged's two-day trips (about Sinai; it is the traditional site of Moses' burning bush (Ex. 3:2).
Most of the desert tours are rugged (the ascent up Mt. Moses alone is by 3, 000 steps and takes three hours), requiring, at the very least, sturdy walking shoes.
Eilat itself, while it's a frontier town (at the junction of Israel, Jordan, and Saudi Arabia) whose recent history dates only to 1959, has all the pleasures of a modern seaside resort.
On a winter day, the sun hits the water like a large yellow ball and bounces back in millions of sparkling rays. There's more than enough of them for all the sunbathers lining the water's edge. There are a marina and a lagoon for sailors and water skiers; restaurants offering French, Moroccan, Indian, Chinese, American, even Israeli dishes; discos; shopping; and a wide range of accommodations, most with pools or on broad beige beaches: There's a Club Med here; a youth hostel (you don't have to be a youth to stay there); camping sites; pensions; and several hotels rated four star: on the north shore, near the marina and lagoon, the Caesar Eilat and the Queen of Sheba, and south of town, the Laromme. It's on Coral Beach, near the nature reserve and the observatory.
You'll find a museum on the observatory grounds, with specimens of shells, coral, and other local aquatic life. Too, there is an aquarium of the usual sort , with real fish and painted backgrounds.
Interesting as that is, though, it isn't nearly as interesting as watching the fish in their own habitat. It's the underwater observation room that makes Coral World unusual; look through its windows at the local residents dressed in their many-hued finery and you know that the seascape those windows frame isn't just any watercolor.