Which compound is responsible for the borax bead test?
A little chemical detective work gives a plausible answer.

Say the metal is cobalt and it's oxidation state is +2.  Then, with the cobalt calcined to the oxide, you have two possible acid-base reactions:

$\ce{CoO + 2 NaBO2 -&gt; Co(BO2)2 + Na2O}$

$\ce{CoO + B2O3 -&gt; Co(BO2)2}$

Both reactions look good, but upon further review the first one gives something we recognize as a powerful base, more likely to be a reactant than a product.  Moreover,  a quick check here reveals that boric oxide has a low enough melting point to liquefy in the flame, favoring the second reaction kinetically.

So the second reaction above is really the only plausible one.