Examples of excise taxes based on percentage of price keep turning up. Here’s a list:
1. The Confederate Civil War taxes, listed below. The Union taxed liquor by potency – cents per proof gallon.[1] I don’t say that the Union’s choice of tax base explains the victory, but I do suggest that the Confederacy’s choice of tax base illustrates how primitive that “nation” was;
2. Rental car and hotel room taxes – imposed on services, not goods (some folks might not consider that an excise, but it’s a higher than normal rate);
3. The 2.3 percent tax on medical devices in the Affordable Care Act — a tax that is barely hanging on in the face of repeal efforts. That tax acted to take back benefits the ACA gave that folks thought were too generous — like applying the brake because you know you are pushing too hard on the accelerator but don’t know how to calibrate that pushing.
4. Taxes on prostitution, like the 19-percent excise tax in Holland: http://www.huffingtonpost.com/2011/01/12/dutch-prostitutes-taxes_n_807843.html
5. The Federal tax on cigars, 52.75% of sales price but not to exceed $402.60 per 1,000. http://www.ttb.gov/tax_audit/atftaxes.shtml. I’m trying to figure out why liquor, wine, beer, cigarettes, snuff, chewing tobacco steer clear of price base, but not cigars. Friends in and out of government are guessing it’s the inertial influence of former Congressman Sam Gibbons, who represented Tampa, Florida. Or maybe the influence of the Cuban community in Florida now.
6. Today’s marijuana taxes in Washington and Colorado and in California localities.
I’m wondering whether percentage-based excise taxes on goods are a good idea. I’m studying that issue.
Here’s a list of items the Confederates tried to tax at 25 percent:
Alabaster and spar ornaments; anchovies, sardines and all other fish preserved in oil.
Brandy and other spirits distilled from grain or other materials, not otherwise provided for; billiard and bagatelle tables, and all other tables or boards on which games are played.
Composition tops for tables, or other articles of furniture; confectionary, comfits, sweetmeats, or fruits preserved in sugar, molasses, brandy or other liquors; cordials, absynthe, arrack, curacoa, kirschenwesser, liquers, maraschino, ratafia, and other spirituous beverages of a similar character.
Glass, cut.
Manufacturers of cedar-wood, granadilla, ebony, mahogany, rosewood and satin-wood.
Scagliola tops, for tables or other articles of furniture; segars, snuff, paper segars, and all other manufactures of tobacco.
Wines–Burgundy, champagne, clarets, madeira, port, sherry, and all other wines or imitations of wines.
http://docsouth.unc.edu/imls/19conf/19conf.html (search for brandy).
[1] Tun Yuan Hu, The Liquor Tax in the United States, 1791-1947: A History of the Internal Revenue Taxes Imposed on Distilled Spirits by the Federal Government (New York: Columbia University, Graduate School of Business 1950), page 37.
The Center for New Revenue 
Publication 510 discusses a number of excise taxes. I know that at least one (a tax on some fishing gear) is figured as a percentage of sale price by the manufacturer or importer at 3%. It has been around since the 1950s. It is funny that it has been around this long and is at a higher rate than the tax on medical devices but we have never had it considered a threat to the republic or a harbinger of socialism. Maybe it was the start of creeping socialism that creeps very slowly.