Combine The Garlic, Raisins, Onion, Tomato Paste And 1/3 Cup Of In A Food Process Or Blender. Process Until Smooth. Transfer The Mixture To A Large, Heavy Saucepan. Add The Banana And Another 1/3 Cup Vinegar To Processer, Mix, And Add To Rest Of Mix In Saucepan. Add The Remaining 2/3 Cup Vinegar, Water, Brown Sugar, Salt And Cayenne Pepper To The Saucepan. Bring The Mixture To A Boil Over Medium-High Heat, Stirring Frequently. Reduce Heat To Low And Cook Ketchup Mix, Uncovered, Stirring Occasionally, For 1 1/4 Hours. If Mixture Becomes Too Thick, Add Just Enough Water To Keep Mixture From Sticking But No More Than An Extra Cup. Add The Corn Syrup, Allspice, Cinnamon, Nutmeg, Pepper And Cloves To The Ketchup. Cook The Ketchup Over Medium-Low Heat, Stirring Frequently, For 15 Minutes Longer, Or Until It Is Thick Enough To Coat A Metal Spoon. Stir In The Rum. Remove The Ketchup From The Heat And Let It Cool A Few Minutes. Force The Ketchup Through A Fine Sieve To Strain It, Pressing Down Hard On The Solids. Remove The Ketchup From The Heat And Let It Cool To Room Temperature. Store The Banana Ketchup, Covered In The Refrigerator For Up To 1 Month.