The subject Taking and filming hikes uses conjunction reduction where both verbs share a common object. It’s exactly like saying Taking hikes and filming hikes.

However, that brings us no closer to an answer as to which of these two to use:

1. Taking hikes and filming hikes makes me tick.
2. Taking hikes and filming hikes make me tick.

In fact, there can be no right answer to the question “Which one is correct?” here where one possibility is always right and other always wrong. As with so many things in human language, either one is acceptable, but they say different things. What they say is whether the speaker considers them one thing or two things. Actual corpus samples indicate that both occur. Singular concord occurs when the combined subject is thought of as one concept, and my own personal preference is to use singular concord in this instance.

These examples are all from Google Books. The subject I will use bold for and the verb that agrees with the subject I will use bold italics for.

• For most of us, eating and drinking is a pleasure, and an important opportunity to meet socially with friends and family
• Mindless eating and drinking is the source of most excesses, as well as the harmful effect on chronic disease processes.
• Eating and drinking is now an end in itself.
• Eating and drinking is also a feature of cultural and religious rituals and ceremonies.
• Likewise, because it involves eating and drinking, this eating and drinking is viewed as not ordinary eating;
• The gratification and reward of eating and drinking is unmistakable.

But:

• Eating and drinking are enjoyable as well as being essential to our health and well-being.
• Perhaps the most frequent and regularly performed of all rituals, eating and drinking are integral to everyday life.
• Eating and drinking are much more than ways of satisfying hunger and thirst.
• Discontinuation of fluids is normally on medical orders and in terms of rehydration, this often occurs when eating and drinking are established.
• It is unquestionable that eating and drinking are activities required to sustain life.

Summary

So there is no one answer that fits all cases. It’s up to the speaker to say it however they’re thinking of it.

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In case our asker Rosita knows Spanish....

Your screen name here, Rosita, is commonly one of Spanish derivation. So maybe you know Spanish. Let me therefore further note that notional concord also occurs in the corresponding Spanish versions.

Again from Google Books, first with singular concord in the italicized portion. (Spanish uses only infinitives as verbal substantives for subjects and objects, never gerunds which can only be modifiers in Spanish, so these examples are necessarily -er verbs not -iendo ones.)

• El comer y beber no es solo una necesidad física, sino que es también un elemento importante en el tejido de toda sociedad.
• Los deseos y las aversiones son notables; el comer y beber agrava todos los síntomas.
• El el texto que meditamos, no es permitido decir que el comer y el beber sea un comer y un beber improprio y alegórico.
• En el Norte necesitan comer y beber mucho para estar alegres, para sentir el calor de un sol que falta; en el Mediodía el comer y el beber pone sentimentales y planideras a las gentes.

And then with plural concord:

• El comer y el beber deben obtenerse mediante el trabajo.
• El comer y el beber han sido percibidos siempre como numinosos, es decir, como acciones que despiertan en nosotros un «sensus numinis», un sentido de lo Otro, de lo sagrado; como experiencias hierofánicas del Misterio.

So even in languages with a stronger and more consistent inflectional morphology and concordance in number between verbal subjects and objects and their corresponding verbs and adjectives do we see the idea of a conjoined subject sometimes taking singular concord and sometimes taking plural concord.

It all depends on the speaker’s intent, just as in English.