Oscillating reactions and blood got me thinking (and I'm sorry if this is in any way offensive):
St Januarius has a holy relic in Naples that supposedly contains his blood. Once a year, it is taken out for a week and supposedly turns from solid clotted blood to liquid, then back again.
There are a bunch of theories that try to explain it, but the two that would work best for you are
A) it contains a low melting point wax or oil.
B) it contains a thixotropic gel. (Shear stresses liquify it) ,
Both scenarios would be good, the first if you got a wax with a melting point around 75-80 degrees or so, and used a heat conducting wire, her body heat would warm it throughout the evening.
Vaseline by itself might be good, and you can add wax to it to raise the melting point, or it to wax to lower the waxes melting point. A bit of experimentation would be in order to find an optimal melting temperature.
The second, if you had them dangle, the swinging action would do the same.
Have an article showing how it could be done: http://www.scientificexploration.org/journal/jse_06_3_epstein.pdf
In both the coloring agent would be iron oxide.
No actual use of any corporeal donations, and I know that was the point, but in case you can't come up with anything else, it would at least be an interesting conversation piece.