By what mechanism does elevated homocysteine level accelerate thrombin formation?
According to a heavily-cited paper (below), homocysteine reduces the expression of thrombomodulin on the surface of endothelial cells. 

Thrombomodulin binds to thrombin, and the resulting complex does not promote coagulation, but instead activates protein C. Protein C has an anticoagulant effect. Thus reduced levels of thrombomodulin will result in increased levels of free thrombin (promoting coagulation) and in reduced levels of protein C (also promoting coagulation).  

I haven't found any evidence that homocysteine has an effect upon thrombin formation directly.


  Lentz,SR and Sadler, JE (1991)Inhibition of thrombomodulin surface expression and protein-c activation by the thrombogenic agent homocysteine. J. Clin. Invest. 88:1906-1914
  
  Abstract Elevated levels of plasma homocysteine are associated with both venous and arterial thrombosis. Homocysteine inhibits the function of thrombomodulin, an anticoagulant glycoprotein on the endothelial surface that serves as a cofactor for the activation of protein C by thrombin. The effects of homocysteine on thrombomodulin expression and protein C activation were investigated in cultured human umbilical vein endothelial cells and CV-1(18A) cells that express recombinant human thrombomodulin. Addition of 5 mM homocysteine to endothelial cells produced slight increases in thrombomodulin mRNA and thrombomodulin synthesis without affecting cell viability. In both cell types, thrombomodulin synthesized in the presence of homocysteine remained sensitive to digestion with endoglycosidase H and failed to appear on the cell surface, suggesting impaired transit along the secretory pathway. In a cell-free protein C activation assay, homocysteine irreversibly inactivated both thrombomodulin and protein C in a process that required free thiol groups and was inhibited by the oxidizing agents diamide or N-ethylmaleimide. By inhibiting both thrombomodulin surface expression and protein C activation, homocysteine may contribute to the development of thrombosis in patients with cystathionine beta-synthase deficiency.